I've been to the MC several times w/ my kids.....last summer for a week. Some of the "freebies" and discounted places/events that my kids loved....
1. Just hanging out in Central Park (easy walk from the MC). We brought a nerf football, and the kids threw ball, climbed the rocks, and played on the playground. My daughter (now almost 14) is a huge dog lover....and enjoyed watching the people walk their dogs.

Also, in the summer, there may be free concerts in many of the parks around the city. Last year, we saw several "shows" in Bryant Park----snippets of songs from some of the best on Broadway.
2. Staten Island Ferry ride ....FREE....and gives a great view of Statue of Liberty and NYC skyline. Plus, some much needed "rest time" from hustle & bustle of the city.
3. Kids (even at their "preteen" ages) loved visiting Toys R Us, FAO Schwartz and the Nintendo Store. Lots of areas where they can "test out" the various toys. Surprisingly, my kids didn't beg for any toy...they just enjoyed the experience.
4. Chinatown---my kids just loved walking through the area, bartering w/ the street vendors, (on one visit, my son was into "Pokemon cards", and found some "deals"). Also cheaper eats than in midtown.
5. We tried to use public transportation---walked or took the subways and buses all over the city. I know kids ride free (up to a certain height), and my kids loved the experience.
6. Museums---try to find discounts via AAA, or if there is a "tourist card" that would be worth your while. The new Sports Museum in lower Manhattan was a big hit last year, as was the Museum of Natural History. I did drag them to the MoMa (free evening), and tried to make a game of looking at the paintings and coming up w/ their own "titles". Of course, my youngest son just giggled through all the (semi)nude paintings & sculptures.
7. While everyone visits "Empire State Building", we actually prefer the "Top of the Rock". Lines weren't as long, views were nicer.
8. We prefered to eat in local pubs and smaller restaurants, and often picked up fresh fruit either from the local stands, or a nearby grocery store (several within walking distance of MC). Usually, we ate one meal out each day (usually lunch,since it's cheaper);then ate leftovers or sandwiches & fruit in the room. Oh....and my kids learned to drink water in restaurants....those $3-4 sodas can really add up. (I told them the money we saved would go towards their souvenirs).
My kids really just liked soaking up the sights of the city---whether it was a group of kids performing a dance on a street corner, the mounted policeman, the horse drawn carriages in Central park, or a glimpse of "The Naked Cowboy"
You will have an awesome time!
DEB