Manhattan's Chinatown is my second favorite neighborhood next to Fort Greene. It's full of people, odors, bars, clubs, cafes, and restaurants. There's always something going on here.
Moma is worth a visit, but for a more lively Art experience ánd for free, one should visit Chelsea. A colony of 400 Art Galleries, showing the best in contemporary art. Running straight through is the high line, a 1 mile long linear park, build on a former railroad-spur, worth the walk.