How do you make your children fall in love with a place like New York? When David Usborne moved to the most exciting city in the world (for grown-ups) his offspring weren't at all keen on the idea. Well, it's work in progress

They had a point, of course. Until then, I had been living in upscale Greenwich, Connecticut, not far from what is still their main home with their mother. By moving to New York I was ending my enslavement to the commuter routine and gaining the alleged privilege of a Gotham address. But I was also accepting a standard of living that most sane people might consider seriously wanting.

Polly, who was just 10 at the time, had another concern that seemed reasonable to her. Would she be safe? Though she had visited many times, of course, her image of New York was still largely informed by its old reputation for violence - Rudy Giuliani and his crime-stopping achievements were hardly familiar to her - and by the police dramas on television. It was a happy coincidence that my apartment building happened to sit directly opposite a large police station. What could be safer, I asked?

While their reticence worried me, I still felt confident that Manhattan was a bit like spinach. As the children grew older they would eventually come to enjoy its flavour. They would soon be teenagers, I reasoned to myself. In fact, Jonathan already was, if only just. They would quickly catch the bug. Wouldn't it be kind of cool to have a Dad living in New York City and spend some weekends there?

A few side-effects I had not anticipated, however. All parents who are separated and who have only limited time windows with their children face a common problem: when they are with you they are away from the usual network of friends and activities. You hope they will make friends where you live, too, but that is hard to make happen - especially so in this town. I have seen one other child living in my entire, seven-floor building. In fact, she is on the same landing, but she and Polly have yet even to look at each other.

What this means is that when they are with me, it is essentially just them and me. (And, I should say, the pug.) Most often it is in fact only Polly and me, because Jonathan spends much of the year at school in England. Meanwhile, the dimensions of the apartment compel us to get out of it as much as possible - school homework and the allure of the million-channel cable television notwithstanding. What happens when we leave it? We become instant tourists in New York - without the jet lag.

If I am living in a foreign country I never quite shake the feeling that I'm still almost on holiday there, even if it has been years since I arrived. I am still that way about America and all the more so about New York. Even the simplest of outings with the children give me a little shudder of discovery. A walk with the dog along the newly refurbished runner's path on the East River or even a supermarket outing can get my expeditionary juices running. And the pleasure is doubled if I think I am sharing something exciting with my children. Never mind if I am probably deluding myself in that respect most of the time.

The impression I hope my children will eventually get is not that New York is simply over-crowded, over-congested and generally overwhelming - it is all those things, of course - but rather that is overflowing with things that will capture their attention. Here all the clichés about Gotham apply - the big buildings, the crush of ethnicities and languages (immigrants from 176 countries live here), the weirdos in the streets, the straight people and the gay people, the baseball, the music, the theatre shows. And on and on. I want them not to be scared that the homogeneity of suburban life has vanished but to savour it.

Just this last weekend, Polly had a dose of New York that might have caused her indigestion. Simon, my nephew from London, was in town so we went into tourist overdrive. I was even silly enough after dropping by the Sony shop at the company's US headquarters on Madison Avenue to pack the three of us into an open pedi-cab. We were only going six blocks, to the flagship store of American Girl Doll on 49th Street - a must-stop, though a potentially ruinous one, financially, for most young girls of a certain age. But I commanded our pedalling pilot to take a long way around, passing the Waldorf on Park Avenue. Polly later confessed that she found riding around on a glorified tricycle in public rather embarrassing.

Instead of going to the cinema on Saturday night like usual (I am dying to see Wallace & Gromit), I dragged them out again for a "surprise" outing. Beware of seasickness, was all I'd say. Instead of a boat on the Hudson River, we arrived at the new planetarium, known as the Rose Center, attached to the American Museum of Natural History. I love the architecture - a giant globe in a glass cube - but, more importantly, on weekend nights they give the place over to a show that combines rock music with a 30-minute orgy of strange and psychedelic images projected on to the dome. Called SonicVision and created by Moby, it was more for Simon than Polly. If it made her queasy, she didn't say a thing.

Most people who live here will tell you they barely scratch the surface of the things there are to do, and that certainly applies to me. I go to the museums and galleries far less often than I should. That is also true of Broadway, but the reason is a bit different. I can't afford the $100 tickets. I have no such excuse for off-Broadway shows, however. On Sunday, we made amends, finding a matinée performance of a musical called Fools in Love, loosely based on A Midsummer Night's Dream. It was outrageous, zany, gender-confused and often downright silly - and Polly adored it. When we left the theatre on Mercer Street in SoHo, we headed straight for Joe's Shanghai, a restaurant on Pell Street in Chinatown that has become a favourite with Polly and me, because of its fantastic soup dumplings.

It is the sheer variety of possible experiences that Manhattan offers us that is so exhausting and so rewarding. If the sun is out we can take the pug to Central Park, linger with him at the dog run in Union Square or Washington Square Park or grab a ferry to Staten Island. If it's cold, there is the cinema or Joe's Shanghai or about a thousand other restaurants of different flavours within a short walk or subway ride.

I couldn't swear that either of my children is yet any more in love with Manhattan than they are with spinach. But I am doing my best to make sure it happens to them sooner or later.