There aren't really any theme parks in New York City but there are plenty of things for kids to do, even in the winter. You can always take them to a Broadway show. Right now, one kid friendly show is "Elf" based on the movie starring Will Ferrel.
Central Park offers ice skating as well as a few jungle gyms to roam around. Toys R Us in Times Square is usually a good hit as it has a giant ferris wheel inside the store. Ice skating is also available at Rockefeller Center which also offers tours of the NBC studios.
You can go to the top of the Empire State building and pay your respects at Ground Zero. Up in Washington Heights there is another park, known as the Cloisters which offers many paths for running and playing. Magnolia is a rather famous cupcake bakery with a location near Rockefeller Center now to enjoy treats and lunch in Grand Central Station is often fun.
The station is not only large, but it is fun to watch the trains come in and out for most kids.
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