[DonRotolo]

I definitely second the following:

Circle line around NYC (but not if it's really hot out)
Dylan's candy bar (Buy & eat a Violet Crumble - very sweet, and unique)
Chinatown (not in the rain). Hong Fat's is great.
the Intrepid
American Museum of Natural History & Hayden planetarium (if it's hot or raining)

Then there's....
Ray's Famous Pizza - REAL Pizza.
Have a bagel, anywhere. With a schmear (cream cheese).
South street seaport, and walk over to Wall Street, just to see it.
And come on over to Jersey - you can walk across the George Washington Bridge (about a mile) - very cool, and the other side is Fort Lee historical park, at the top of the famous Palisades.

Oh, and definitely take the subway (daytime only!), it's cheap enough, and the A/C often works. Well, sometimes.

Don