Chelsea Market is a phenomenal place for all foodies! It's situated on 9th Avenue between 15th & 16th Street in Meatpacking. If you can't find it here in the seafood market it simply doesn't exist - there're everything from Arctic char to wahoo. You can also eat on the spot ready-made meals or take fantastic ingredients home and cook yourself.
Btw, Diane von Furstenberg's flagship is very near there...
The small Food Market on Broadway at 34th Street is a nice place to have lunch outside or to take away.
The Farmers' Market at Union Square is not bad either. Full of gorgeous fresh mostly organic local products.