1. See as many live bands as possible.
2. Go to as many museums as possible. Still haven't been to the Museum of Natural History or the Museum of Modern Art, among many others.
3. Go to an art opening.
4. Have a picnic in Central Park.
5. Go to Ellis Island.
6. Visit and do something cool in all the boroughs.
7. Sun bathe in Central Park.
8. Be in the audience of a show taping. Something like SNL, Daily Show or Colbert Report will do.
9. Look for cool local bars/restaurants.
10. Go to the opera, ballet or to see the Philharmonic (or all of them).
11. Compare New York beaches to Florida beaches.
That's all I can think of right now. Did I forget something? Let me know.