New York is full of fun activities that can keep you and your kids busy from sun up to bed time. New York City has a childrens museum, themed playgrounds, shows for all ages, street performers, amazing sites that offer great views from above the city like the Statue of Liberty or the Empire State Building. There is always FAO Schwartz, the largest toy store, or a nice trip through central park to play with the horses. Visit one of the many dog parks and watch them run about. A nice day of fishing, playing with a remote control boat or feeding the ducks in central park is also a nice afternoon. Visit the Guggenheim and walk up the spiral ramp while enjoying some works of art. Maybe buy tickets to see such amazing shoes as the Blue Man Group, a wonderful show for all ages that has made waves around the world.
There are more than enough things to do in New York City to keep you and your children entertained. There is no reason for you to use them as an excuse to not make a vacation to the wonderful city that never sleeps. The best way to experience this city with children would be to to stay in one of the thousands of New York short term rentals located all over the city. These offer a more home-like atmosphere for you and your children to make them more comfortable throughout your vacation.