Cuisine, location, price range (including tax, tip, and wine/drinks)? Hard to make a recommendation without knowing more. Many of the top fine dining restaurants in NYC will be closed; however, Jean George and Le Bernardin will be open.
According to Zagat, these will be open:
Adour, Armani Ristorante, Benoit, BLT Market, Blaue Gans, Carmine's, Cornelia Street Cafe, David Burke Townhouse, Fishtail, Kittichai, Le Bernardin, Macao Trading Co., Rouge Tomate, SD26, Tamarind
Additionally, Ma Peche, Momofuku Ko, and most Jean George restaurants incl. Jean Georges (main dining room and Nougatine), Perry Street, etc. will be open.
I'd check Opentable.com and/or start calling around NOW to book your table ASAP.