We loved NYC. My siblings and I went with my parents for the bowl game. My mom who hates traveling (for the most part) and cities loved it. My dad said if he was 40 years younger, he would have liked to move there.
Some things I loved--
1. If you can see a Broadway play, I'd recommend it. Tickets are pricey, but worth it.
2. Ellis Island is really cool. Not sure if it is reopened yet.
3. Walking across the Brooklyn bridge
4. We stayed at the Hilton right next to the WTC and didn't have tickets for the memorial. We could see it from our room though. Anyway, there is a little, tiny church right around there that for whatever reason didn't get damaged. There are exhibits and things in that church. Well worth your time to step in there.
5. Macy's was pretty fun to see.
6. Wall Street/Battery Park
7. Walking around Central Park and Bryant Park