Also, tours are tacky for the most part but allow you to get all the touristy stuff done quickly. I really love wlaking tours - google "Big Onion Tours" - they're quirky, cheap, and offer lots of secret info, like we visited a hidden courtyard in the Village frequented by Edgar Allen Poe plus found out some nifty stuff about washington sq. park. I was born here but still took the tour since it was a great way to spend a sunday afternoon (the tour guides are really charming, I think mine was a stand up).
Food:
Indian - Tabla, great fushion cuisine
Chinese - just go to china town (R to Canal St.) and walk around.. Bing Wong (shut up) is a favorite dive of mine - their roast pork is sooo good.
Neighborhoods to visit:
China Town
Greenwhich Village - key historical places include the stonewall bar (starting point of the gay rights struggle), and the whole neighborhood, really.. ACE trains to west 4th.
East Village - former punk rock haven, now a good place to find good dives, I like the thirsty scholar, blue and gold (a historic dive), and punk rockish clubs such as riffiffi and lit that have recently been over run by hipsters. Fun to see the pierced and tatooed set, even if you just want to laugh at them - R train to 8th street, F to 2nd ave.
Murray Hill - lots of good indian food there, including a few indian/chinese hybrids
Central Park should be visited...
SoHo (R to Prince, F to Broadway/Houston) - Chic little boutiques, great shopping.. Some nice lounges. I like the Mercer Bar, on Mercer. Across the street is this lovely tea room - it's very chic and not so pricey.
Brooklyn
Williamsburg. I liked this a lot more when I was 20.. But now I kinda hate the people who live there.. Good place to find live music though and lots of cafes. Sea is a nice, hip, and fun thai place that's CHEAP but seems expensive (they filmed Garden State's "LA restaurant" scenes there)... L train to Bedford Ave.