Yippee!! Good for you, you will have a great time in NY. Union Square farmer's market on Saturdays.
Here are a few restaurants, we don't get in to the city that often, so we tend to splurge when we do.
Over the top/VERY special occasion:
L'Atelier Joel Robuchon: exquisite food and prep detail, if budget is no object (In the Four Seasons Hotel)
Nice:
Grammercy Tavern--excellent
Toqueville
David Burke and Donatella
Picholine
Union Square Cafe
Scalini Fedeli
Avra Estiatorio (beautiful Greek, specialty seafood)
Eleven Madison Park
WD-50: really unusual food
Casual:
Metrazur (in Grand Central Station) worth going to see GCS
The Pearl Oyster Bar: Greenwich Village
(great lobster roll sandwiches and skinny fries)
Butter
Little Italy:
Il Palazzo
Angelo's: great gnocchi