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…