If they are not old enough to be into the museum's crusading four Rs - reduce, re-use, recycle, rethink - they can visit a new exhibition opening next week, called "The World of Pooh", devoted to the AA Milne stories that are a children's favourite on both sides of the Atlantic. Or they can get in training for one of the city's most popular adult pursuits, by wheeling a supermarket trolley round a pretend shop. If those do not appeal, they may like to have a story read to them at the literacy centre upstairs, or get involved with strange sounds and sweet music in a new exhibit by the name of "Soundsfun".
When looking for a place to take children on holiday, New York may be among the last cities that spring to mind. It is famed as a playground, certainly - but principally an after-dark playground for grown-ups, with theatres, restaurants and nightclubs that throb with adult life. Its reputation for sin and danger may discourage concerned parents from exposing their little ones to it.
Yet hundreds of thousands of children live happily in New York, and the city is packed with facilities for them and for young visitors. At weekends, clowns and other entertainers throng Central Park, giving impromptu shows. A zoo is close at hand, where penguins cavort merrily in a glass-walled pool; one of the world's best toy shops, FAO Schwarz, is just outside the park on Fifth Avenue.
The Children's Museum of Manhattan is one of two in New York of a kind that has no exact equivalent in Britain. The other one is in Brooklyn. They are not the same as museums of childhood, which feature historic toys and games. Children's museums, American-style, have few static exhibits but are centres for instructional and enjoyable activities, based on the assumption that children of all ages prefer to do things rather than to stare at objects.
"Get to Know Your Trash" is a typical exhibit - earnest, imaginative and involving. Children love the part where they fish for metal cans with magnets, learning as they do so the difference between aluminium and tin. It is part of the Sussman Environmental Centre in the museum's back yard, made up of displays and demonstrations about the mechanics of city living.
In the yard is a three-storey urban tree house made of recycled rubbish, containing interactive exhibits encouraging care for the environment, described in the explanatory material as "a replica of the urban ecosystem". It includes a working model of the city's water supply. Rain, produced magically when children rub their hands together, fills reservoirs, then flows through pipes into buildings and drains, and eventually - duly filtered - into rivers and the sea. There is an explanation of compost heaps ("Hot Rot") and a demonstration of how to make recycled paper.
"Kids need to touch and experience," says Suzie Hayne, former head of public relations at the museum. "It's an integral part of learning."
That was the philosophy behind the opening of America's first children's museum, in Brooklyn in 1899. The Brooklyn Children's Museum still exists, though not in its original premises. For years its most popular attraction has been a tremendous water feature in the entrance, where children use wooden bricks to build dams and divert the flow, learning how rivers work and having an enjoyable splash around at the same time.
In the early years of this century, several museums added activity centres for children based on the same participatory principles - the Science Museum in London has an excellent one. But not many dedicated children's museums were built until the 1970s, when they sprang up in several American cities. The Manhattan museum opened without permanent premises in 1973, under the unwieldy name "Growth through Art and Museum Experience", or GAME.
New York was going through a fiscal crisis. School budgets were being slashed, with arts and music hit hard. GAME worked with schools to help remedy that. Soon it won funding from charitable foundations and the Federal Government, and broadened its work to appeal to the whole community, not just schools. It found premises in midtown.
In 1984 it changed its name to the Children's Museum of Manhattan, and in 1989 moved to its present site, a former private school on the Upper West Side. Though school groups are still very much in evidence in term- time, most children now visit the museum with their parents or other adults. Of its 200,000 visitors a year, 55 per cent are grown-ups.
"It's important to engage children and adults together," says Robert Blandford, the museum's associate director. "We encourage active involvement by parents. They can't leave their children here and go away.
"Most of our visitors, obviously, are people who live in the city - but we do see a number of tourists and their children, and we welcome that."
Many temporary exhibits and activities are based on popular juvenile books and their characters. When I was there, children were absorbed in a display linked to Maira Kalman's series of books about Max ("a poet, a dreamer, a dog"). There were games to play in which he figured, and children were trying their hand at writing their own stories about Max, and drawing pictures of him. Another exhibit is devoted to Tar Beach, a book about an eight-year-old girl who flies to the stars from a Harlem rooftop.
The fun parts are mixed with socially useful programmes: there are dedicated facilities for teenage mothers and their children, for families in city- run welfare homes and for children who do not speak much English. If this seems to give the place a slightly preachy air - the dread words political correctness come to mind - it is not so pervasive as to be a deterrent. To promote the virtues of recycling and of trying to get on with your neighbours does not amount to dangerous brainwashing.
It is hard to say whether museums like this point the way to the future, or whether they are already a little old-fashioned. Some fear that the combined effect of television and home computers, and in particular the growth of interactive CD-Roms, could quickly make them redundant. Mr Blandford is not among them.
"People come here for people," he believes. "They come because other people are here. It isn't Disneyland - but with a TV at home, you can't sit on the floor with other kids and learn how to make something, then take it away with you afterwards."
! The Children's Museum of Manhattan is at 212 West 83rd Street, New York, NY 10024 (00 1 212 721 1223). Open daily except Tuesday.Reuse content