A few "musts" for NYC with children:
1. Ride the subway. Very safe, very fast, very cool. Yes, you will get turned around. Yes, you will meet some interesting people. But it's very cheap ($2.25 one way--with as many stops as you want, and children ride free) and a fast way to get around the city. And as long as you stay in the Manhattan area you will be fine.
2. Stop at Grand Central Station--just like the movies. Free to look at. :)
3. The Natural History Museum--very awesome. They have "suggested" prices for admission ($16 for adults, seems like $8? for children) HOWEVER you do not have to pay that much. They ring you up and give you the suggested price and you offer to pay less. Our family would have cost about $50, I only paid $20. Technically, you could pay $1.00 (or nothing I guess) a person and they would have to let you in. I think it's well worth a $5.00 per person admission--I think it's worth the $50 we would have paid, but we're thrifty. We only got through the 1st and 4th floors--and we stopped very briefly to see DumDum from the movie "Night in the Museum"on the 3rd floor. It was very nice and very cool. Animals, dinos, gemstones, etc. My kids LOVED it.
4. FAO Schwarz and Toys R Us. Two huge stores--very cool for children. FAO has create your own Muppets and Barbies that my girls thought were cool. Toys R Us has a ferris wheel. Inside. Crazy.
5. Rockefeller Center--just like on tv. Skating rinks, tv broadcasts. Go underneath and it's a little shopping area.
6. Get lost and wander around Central Park--free and fun. If you walk along the 5th Ave side you'll see some cool houses and shopping.
7. World Trade Center. If you ride the PATH transit--cheap train ($1.75 per person, kids free) it takes you right to the site. You can also see the construction for the new memorial.
8. American Girl Store. If you have a girl you should go. Trust me. 3 floors of babies, dolls, and clothes. Wow. Molly is a new fan.
9. Times Square. Lots of lights--but can be overwhelming with the people and noise for young children.