When I go, I make a point to go to Peter Lugar's Steakhouse in Brooklyn, and have some local specialties like the pizza and Pastrami sandwiches.
For enterainment, there's a warship if you're into that, off-broadway is nice. It's a great walking city, there's this one nice neighborhood I forget the name, maybe Greenwhich?
I think I heard a lot of gays moved there, I mention just for identifying it. Nice shops etc.
Watch out for scammers. Once a bus dropped people off from the airport and a guy pretended to work for them, helping with luggage, offered to change a $100 bill... bye.
The Metropolitan Library is a great visit. Art stores next to Central Park.