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.
The reputation of Mission Chinese Food is for being cool, weird, and extremely eccentric, which tends to mean that you either love it or hate it (an assessment that is at least somewhat correlated to your personal tolerance for spice).
The oldest still-operating restaurant in New York City, still in the family of the original founders. At Christmastime, it's decorated to the nines. Go with a big group: portions are large and the wine flows liberally. Look for the little buttons on the walls: in the old days, the mafia would hang out in the back room, and if diners saw the cops come in, they'd press the buttons so the mafia guys could run out the back.
This park sits halfway between my apartment and my studio. I spend a a lot of time hear sketching and making phone calls. The trees are beautiful during spring and fall.