1. Head down to the village near NYU.
2. Take a walk in Central Park
3. Times Square/Madame tussauds wax museum
4. Chinatown and Little Italy
5. If you go the the Empire State building, it's like, a two hour wait. The Rockefeller building is like, a 15 minute wait, plus it's probably a better view.
6. Ellis Island/The Statue of Liberty
7. Clubs/Bars (if you can get in, they're pretty uptight about ID's)
8. Go to a Yankee game.
9. Go to Brooklyn
10. When you get to Brooklyn, have Brooklyn pizza. Choose one of the first three from this list:
http://www.yelp.com/list/best-brooklyn-pizza-brooklyn.
11. To get back to NYC, walk along the Brooklyn bridge.
I can add some more if you want.