You can ride the Staten Island ferry (for free). Great way to kill an hour roundtrip; and, have a close up look at NY Harbors Statue of Liberty, Brooklyn Bridge, and of course, lower Manhattan.
My favorite passtime: eating.

Seriously, eat at the Boathouse Restaurant in Central Park. Nice views of the lake, and loads of people watching.
Chinatown and Little Italy are really one neighborhood. If you head down there in the evening (to eat)

you'll enjoy a nice NY vibe.