NYC is a great place for all kinds of dining, cheap or expensive or anything in between.
Cheap Eats:
Go late night to CRIF Dog for a great hot dog for like $5.
Sushi:
Sushi Yasuda - book a reservation 25-30 days in advance and ask for a seat at the Sushi Bar in front of Yasuda himself
Tasting Menus:
Del Postro or Gramercy Tavern are both great.
Italian:
Way too many choices, cheaper places down in Little Italy and some great (but more expensive) places in midtown
Classic NY Pizza:
Tons of fights here, I usually take first time NY'ers to Lombardi's.
Steak:
Peter Luger - worth the subway/cab ride to Brooklyn, just over into Bklyn from Manhattan so not a far trip. Its classic NY/Classic Steakhouse at its best. There are other ones in nyc, more modern ones, but for what it is, Luger's is just top notch and classic.
BBQ:
Oddly enough, nothing against Jakesw and his opinion, but I usually steer clear of Dino BBQ - very long lines and way too much sauce on anything I've ordered before. Its also usually very loud in there. I usually stick with Hill Country (especially for Brisket/Sausage), Blue Smoke (for ribs) or sometimes to mix it up I go to RUB. I think Hill Country does an "all you can eat" night sometime early in the week like a Monday or Tuesday night, its a very good deal for the price considering the quality of food.
Due to living in NYC for a while, and my job in sales, I've been lucky enough to eat at many of the bigger "famous" NYC restaurants, so any questions, just ask.