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.
I probably frequent here twice a week, because I am obsessed with Mexican food, and I'm fortunate enough to live in close proximity to this place. Taqueria Tepango is definitely a sapphire in the rough since there are a lot of terrible/over-priced Mexican restaurants in NYC.