Unless you’re going by private Lear jet, hot-air balloon or in First Class, there can’t be a better way to fly to New York than aboard the Bankers’ Express, BA001. Launched last September, it’s the Club World only service that avoids the US immigration queues by stopping briefly in Shannon, Ireland to complete the fierce US formalities and to refuel.

There’s almost enough space on board the plane to play baseball – 32 flat-bed seats (but room for 100 ordinary seats); decent enough food of the asparagus and port reduction drizzle variety; fabulous service (when I flew, if there had been one more passenger we’d have outnumbered the crew); and a cute mobile phone icon which tells you when you may contact Earth.

I powered my laptop, pressed a buzzer for help which arrived within a nanosecond and used enough hot towels to open a Chinese restaurant. Then, seemingly moments later, we touched down at JFK’s domestic airport. Perhaps uniquely for a commercial carrier, I was the only person on the flight with checked-in baggage (is there a social stigma attached to being the only loser who has enough spare time to wait to retrieve checked luggage?).

Next we test drove the Farrell limousine service. This is one of New York’s most expensive car companies, offering a service that is beloved of discreet celebrities, private money and families into their fourth generation of Farrell hire. They have gleaming clean sedans, stretchers and formals, plus vans for the Louis Vuitton and professional-beyond-professional, always-early, often multilingual drivers. (‘It’s the best limo service in Manhattan,’ says The Mark Hotel’s general manager, James Sherwin, sitting later in his office among gratefully signed photos from British royals and Very Important People.)

Our first stop is The Mark, the 1923 über-chic Upper East Side hotel with 100 rooms and 50 suites. It’s fresh from a $150 million refit by Jacques Grange – who boasts the Légion d’honneur and is decorator to Princess Caroline and formerly to Yves Saint Laurent – and reopened in August 2009. It’s more like an impressive contemporary gallery than a hotel, but a gallery where your every need and whim is tended to by an impeccable staff. In this ‘gallery’, renowned designers from Paul Mathieu to Vladimir Kagan have created one-off pieces for the playful ground-floor rooms.

The lobby has a jazzy black and white marble floor and ‘Ge-Off Sphere’ Ron Arad pendant light; there is a witty, cloud-shaped bar by Guy de Rougemont and a herd of pony-skin sofas and bespoke geometric carpet; the restaurant has upholstered bar stools and free standing curved banquettes; and upstairs is a more muted kind of chic. Every time you look there seems to be another well-known face being welcomed by the hotel’s Turnbull & Asser clad staff. Oh look, that’s Woody Allen. And there’s Barbara Walters.

We’re just one block from Central Park (think passing hounds fresh from shampoo and set, with Tina Turneresque accessories and private roof gardens on which to cock their pretty legs) and at the centre of the civilised world, near the Met, the Frick, the Guggenheim and the Whitney. But it’s our elder daughter Anya’s first time in NY and (aside from the sartorial hell-hole that is Abercrombie & Fitch, with its torso-baring shop assistants and Glastonbury-decibel music) Harlem is high on her to-do list.

We sightsee in a Farrell Cadillac stretch, driving around the new look Harlem-meets-Zurich – the former black spot polished up by Rudy Giuliani with his hit squads and now full of smiling policemen thanks to Michael Bloomberg and moved into by Bill Clinton with his office. We pass a bright yellow ‘Sidewalk Sunday School’ van wreathed in balloons: God has moved in mysterious ways to replace the burned-out cars of yesteryear. Then we drive past Sylvia’s Restaurant where the politicians hang out for soul food of pigs’ trotters and gizzards, and which has now become a global food brand.

Back on the Upper East Side we lunch at The Wright, the Guggenheim’s recently opened arty restaurant with an iconic Frank Lloyd Wright museum attached. It’s in a sleek white-on-white space – designed by Andre Kikoski, a leading new-garde architect – with curvilinear walnut walls and a layered white ceiling that echoes the original corkscrew building.

It serves modern American (seasonal, local and sustainable) food cooked by ex David Bouley chef, Rodolfo Contreras. Its 58 seats and communal table are packed. Think signature dishes like green market vegetables with slowly cooked egg and truffle and Michelin-style presentation. I don’t get the benefit of cooking an egg slowly but, hey, the food passes muster.

After lunch it’s time to test drive another car company, Jeff Kaplan’s E-Z Ryder. It’s the favourite of in-the-know Lady Cosima Somerset of Concierge London and NYC fame. (An erstwhile friend of Princess Di and niece of Lady Annabel Goldsmith, Lady Cosima knows how to pick classy wheels.) Outside a big sign in the window of a four-wheel drive reads ‘E-Z Ryder Welcomes Caroline’. E-Z Ryder is a small, family-run business, with its cars with blacked-out windows, and another celebrity car firm of choice.

We do a lifetime of shopping and our accommodating driver seems never to tire of circling the block to avoid parking restrictions. We visit the sort of adolescent must-see emporiums that would exhaust you just wading through their names on a list. Meanwhile E-Z Ryder is a teen dream with its armrest full of candies and gums. And as the parcels and packages pile up, we use the car as a luggage depot. (There’s little better than going shopping with a driver.)

So which shops to recommend? Abercrombie, American Apparel and Victoria’s Secret be damned. My personal favourite and top of the (non-adolescent) list isBellhaus, the new lifestyle store aimed at the working woman and fashionable man. It’s Dover Street Market meets, er, Beach in the City. It sells ready-to-wear (including many American designers) plus accessories, candles, beauty, eye wear, Kilian fragrances, vintage pieces (up to $38,000) and Carlos Falchi daytime totes for $220.

Afterwards we have a sunset hour drink in Andre Balazs’ Boom Boom room at The Standard hotel. With its floor-to-ceiling windows (including in the loo) it enjoys spectacular views up the Hudson River. It’s a gawpingly great room 18 floors above the Meatpacking District with Art Deco-meets-contemporary features. A wannabe Studio 54, it has guest-list only pretensions, waitresses in skimpy dresses, a black-tiled room with triangular soaking tub, vertiginous glass-floored smoking terraces and hype to match.

In the evening, we return to The Mark. At this hour, slinky women in Christian Louboutin heels and fitted faces sit in the bar at low-flying cloud tables. Nearby, dapper men stand with practiced smiles and sky-scraper-deep pockets. As they follow their social X-rays into dinner in The Mark Restaurant by Jean-Georges (Vongerichten), we return to our suite: to a soothing place of custom-made furniture and black and white marble Art Deco bathroom. I could happily stay here for days longer. And just then we hear news of the eruption of the Icelandic volcano. We couldn’t have planned it better…

As we arrive, a baboon is trying to break into our tent. The manageress shoos him away and calls a guard who arrives with his spear a few minutes later. She says our primate friend won’t return unless we offer him sweets, which seems good enough reason to ban sugar from Africa. The frisson we feel increases when we learn that guests are only allowed to their tents accompanied by guards. Welcome to the delightful excitements of Naibor Camp, one of the most exclusive tented safari camps in Kenya’s Masai Mara Game Reserve.

The camp is hidden in a grove of riverine woodland on the banks of the Talek River, enjoying possibly the best location in the Mara. Captivatingly, hippos bathe in the river at the bottom of its garden and can be seen hauling themselves out in the evening. The area has the region’s highest concentration of leopard. Rhino hang out on the south side of the river. Plus it’s strategically placed for the wildebeest migration, being close to all the major crossing sites on the Mara River. And because it’s in the heart of the Mara, there’s wildlife viewing throughout the year.

There’s a small air-strip 30 minutes away for landing private planes (or for charter ones, if you must). Or it takes mere seconds to get here if you come in a Lady Lori helicopter, as did the squillionaire who had our tent before us. The celebrity transport of choice, Lady Lori is renowned for accessing the inaccessible from finding a plant not seen by botanists since the Seventies to offering superlative safaris from the air.

But we’re here to enjoy things from the ground, to explore from an open-sided Land Cruiser the rolling open grassland and Safari Wonderland outside our tarpaulin door. So, accompanied by our guide Daudi wearing Masai suka (blanket) and beaded headdress – we set forth into Animal Disney World. We don’t wish to spend time spotting different strains of the Greater and Lesser Safari Jeep or the hot-air balloons that litter the sky so Daudi takes us off the beaten plain.

We are soon rewarded with a herd of elephant, including mini Barbars gambolling and frolicking in the sun; a band of mongoose; and enough zebra to make a crossing. Then we see one of the world’s most spectacular sights: thousands of wildebeest and zebra crossing the great Mara River. A crocodile hovers nearby. But I have to admit that, in this instance, there are also other predators in sight: the animals are closely surrounded by bands of Homo sapiens and a fleet of four wheel drives.

Our next stop is lunch. It’s nothing like the steak and baked pineapple and custard enjoyed by some back at Naibor Camp. Instead we’re served a truly memorable Out of Africa picnic complete with chairs, table and chest of food eaten under a tree on the open plain under the wide sky. If it’s specifics you want, then imagine delicious chicken drumsticks with rosemary and honey and potato salad, eaten under the ‘sausage’ fruit tree beloved of rhinos and in which the leopard likes to lie with his kill.

Back at base camp and done for the day with the wonders of the natural world, it’s hard not to marvel at some man-made wonders. Take the Little Naibor tented suites with their enormous under-lit, low-floating beds on fig-wood bases, Savannah-sized cream sofas and African wool rugs: contemporary style allied with muted bush colours. And as for the Mess Tent with its rustic fig-wood dining table and chunky bush dining ‘thrones’…well, it’s pure Conran en Afrique. And if such style doesn’t sound like the bush, you should try reflexology in the spa tent…

Naibor Camp is also so eco it makes you weep and recycle your tears of joy. Everything is solar- run. It has safari showers and charcoal-heated irons. It attracts khaki-heeled guests who want to leave the world a better place, families, people who want luxury in the bush and rich businessmen. It’s also popular with honeymooners, sipping sundowners and eating romantic meals privately under the stars. After all, it’s particularly charming at night; candlelit and gas lanterns light the paths as the sounds of hippos, frogs and crickets fill the air. And as you sit chatting about the day’s adventures around that communal table, a camp fire burns cheerily…

From £1868 per person based on two sharing for 3nights on a fully inclusive basis including flights, air taxes, park fees and transfers. Book through Scott Dunn: 020 8682 5000; www.scottdunn.com; www.naibor.com. Lady Lori helicopters can also be arranged through Scott Dunn.

According to Lord Mancroft, there are only three things that you need to learn in skiing: ‘How to put on your skis, how to slide downhill and how to walk along the hospital corridor’. What he forgot to mention is that you also have to learn to enjoy sporting clothes and equipment that cost the equivalent of the Greek national debt just to stand in sub-zero temperatures and suffer height vertigo. And additionally, you need to grasp that you will spend un bras et une jambe simply to break un bras et une jambe. Only a mug would do it. Yet, ooops, I’m winter-holidaying in the ski resort of Val d’Isere.

I’m in Val d’Isere with Ella, my 12 year-old daughter, a genetic aberration who likes to ski 24/7 and would happily slalom backwards down a black run. We’re here because of maternal love and Scott Dunn, the luxury tour operator beloved of celebrities and royals. On first sight, Val looks like toy town after someone has sneezed the best Bolivian cocaine over it, with a pretty layer of snow over footpaths, the Baroque church and traditional Savoyard chalets built from wood and local stone. It’s in a majestic setting and peopled less by fur coats than serious skiers, including the likes of Ben Elton, Peter Gabriel and Coldplay drummer, Will Champion.

If you don’t ski, you can do an array of lunatic snowy things like snowmobile driving (junior Schumacher on ice), driving on ice (Schumacher on ice), ice diving (going beneath the ice of Lac de Tignes, for the truly crazed), dog sledding, snow-shoeing, ice climbing (scaling a frozen waterfall with the aid of ice axes and crampons, I ask you…) and paragliding. Or take scenic flights and vivez la montaigne en helicoptere. Or you can eat, which is what I like to do.

But first to our lodgings. We’re staying in Marie, a lovely chalet which sleeps eight, with an open-plan living-area, roaring fire, exposed reclaimed timber and stone, and Hammam and plunge pool overlooking snow-capped mountains. Marie is one of a family of chalets nestling in a cul-de-sac. (If you want to do the oligarch thing, you can stay next door in Marie’s impressive sibling, Le Rocher. A snip with a starting price of £32,660 a week, it sleeps 14 and has ironic arty décor including groovy chandeliers partout, Alice in Wonderland throne chairs, a technogym and a screen on which to watch films whilst in the pool.) It soon becomes clear that we’re onto something special here. Drivers who whisk you hither and thither are included in the price and there’s one member of staff to every two guests, for who nothing is too much trouble.

Take Thomas Checkettts, the chef in Marie. He cut his culinary teeth working with Gordon Ramsay and so must be used to difficult people. Which is fortunate as I’m keen to follow a macrobiotic diet. Forget raclette and fondue, I want sea-weed and miso soup as my mountain staples. Thomas rises gamely to my Madonna-style aspirations and conjures up delicacies like beetroot jelly, sweet pea granite, and garlic and spinach veloute. But very soon I’m lured to the Other Side by his beautifully-presented gastronomic dishes of foie gras, succulent fowl with rosti and breakfasts of smoked salmon and scrambled egg with truffle oil. Diet be damned!

It would be unforgivably piggy to do nothing but eat. So I raise myself for a sports massage from physio Toby Clifford, who is about ten foot tall and all compacted brawn in army fatigue trousers. He is to deep-tissue massage what crevices are to wrinkles. Words like muscular release, relief and amazing come to mind. In the summer he pummels soldiers for the Ministry of Defence. It’s enough to make anyone join the Army. Then in a fit of further exertion, later I walk to my bedroom for a facial from Pamper Off Piste. Pamper On Piste, now that would be interesting.

Afterwards, I swim in Oxygene, the erstwhile winter Olympics press centre now converted into a sort of Chelsea Harbour Club at altitude. It boasts hydro-massage, sauna, steam bath and Art, including life-size cows in the reception area. Plus there’s a pool where women in black costumes and goggles do fierce lengths. You probably take your life into your hands as much in these lanes as you do on the slopes.

Next day, I go (drum roll) snow-shoeing with guide Michel Gavet and a group. We walk in the silence. The sounds are of nothing but falling snow. In the valley below there’s a dam and a submerged village, the church spire of which sometimes shows above the water. People are skiing like traversing ants on the mountains opposite. There are eagles, white hare, roe deer, wolves (apparently) and trees laden with lichen and snow. It’s beautiful. It’s exhilarating.

We press on. I fall over countless times, often ending up stuck knee-high in snow. It’s no walk in the park; it’s more like an aerobics session for advanced mountain goats. As we pick our way gingerly down steep and slippery snow-covered rocks like lame donkeys, there’s a Virgin Mary in a rocky shrine. A bit like the ones you find on hazardous corners of fatal roads, overseeing the accidents. I’m glad to get back to terra more firma and less slippery.

I head to L’Arolay, a rustic restaurant Savoyard with views over the Isere Gorge, for lunch. Here they serve Cremeaux du Pere Francis (a basket of potatoes and an entire cheese in a box,) which my friend, Jane, polishes off, while I content myself with a family-sized serving of tartfilette and Ella demolishes a cow-sized steak tartare. Afterwards, groaning at the waists, we pop down to the Chevallot patisserie for some gastro-porn: think window displays of tartellette framboise and eclairs and, inside, counters of fougasse and croque courgette, and an eponymous owner who is often voted, ‘best pastry cook’ in France.

Then things take a very curious twist. Give me a map of the pistes, and I usually feel giddy just looking at it but Val d’Isere is a legendary area: 300km of marked runs, two glaciers, 1930 metres of vertical drops and 90 ski lifts. And then, reader, I do it. Under the expert eye of Ken Smith, a moniteur independent, I put on a pair of skis and hit the slopes…