As Jim Jarmusch put it in the documentary Blank City, the address is roughly between Bowery, Avenue B, 14th Street and Houston. This area of the city is steeped in art, film, and music history; so many hugely influential artists, film makers, and musicians still live and work here. For such a small area, I think it's had more concentrated influence on contemporary art and culture than anywhere else.
My favorite Chinese food spot. The best Peking duck! Ignore the C health code rating in the window, they must have made a mistake ;) Also, It's BYOB with no uncorking fee, go crazy.
Nothing is more quintessentially New York than a diner. This eatery not only serves excellent, traditional diner fare, but does so in an eclectic environment that mixes Baroque decadence with Midtown grit.