We live an hour by train from NYC and we love to go into the city with our kids. Lots of fun, different things to see and do. I don't think it's any more strenuous or more walking or more complicated than taking the kids to Disney. You just have to be smart about your planning, like with any vacation.
Some things to put on your list:
Statue of Liberty, you can do 2 ways...go to the island or just 'float' by it by taking the free Staten Island Ferry.
Top of the Rock, I prefer this to the Empire State Building. Less crowded, and you can SEE the ESB from it. Awesome view. Can be a little intimidating for younger kids particularly if it's a windy day/night.
Rockefeller Plaza, there is a Wii store there that appeals to my kids
Sony Wonderlab
Gazillion Bubbles Show
Times Square including the gigantic Toys R Us with the ferris wheel inside the store, giant
Lego sculptures and every toy known to man, the Hershey and M&M stores, the Wax museum
Mars 2112 restaurant (you don't go there for the food, it's ok but not anything to write home about, but the whole atmosphere, theming is great fun for kids)
Central Park including the zoo and children's zoo, carriage rides, RC boat pond, carousel, neat sculptures and more. Centralpark.com will give you a complete list of things to see/do and a map.
FAO Schwartz
Little Italy
Chinatown
Max Brenner's, especially for dessert. Check out their menus, some things for the kids that they offer are a chocolate hamburger with strawberry 'ketchup' and a chocolate syringe you get to squeeze right into your mouth...great fun! Bring wipes!!! LOL
Street fairs and festivals, see the current schedule here and check back for 2010s schedule closer to your trip
http://www.nycstreetfairs.com/sched.html
NYC Fire Museum and the FDNY Fire Store
http://www.nyfirestore.com/visit.html
Children's Museum of Manhattan
American Museum of Natural History
Children's Museum of the Arts (near Chinatown)
http://www.ny.com/museums/children.museum.of.the.arts.html
Bronx Zoo (obviously not in Manhattan but there is, or used to be you'd have to confirm this, a free shuttle from Manhattan and it is a GREAT zoo, so worth it)
Hope that helps!