Lots of great food, especially on Bleecker St. and Carmine St. Keste, Po, Pearl Oyster Bar, Perilla... it really depends on what time you wish to dine, how long you might be willing to wait for a table, and how much you are willing to pay.
Pearl Oyster Bar
18 Cornelia St, New York, NY 10014
9 Jones Street, New York, NY 10014
IFC = International Film Center on 6th Ave. and 3rd Street.
If you're for looking an early dinner before a movie, maybe you can try for walk-in bar seats at Babbo or Minetta Tavern. Po is also in the area.
110 Waverly Pl, New York, NY 10011
113 MacDougal St, New York, NY 10012
Film Center Cafe
635 9th Avenue, New York, NY 10036