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).
Beach approachable by public transportation and can be connected with a visit of MOMA PS1 Art Installation (Katharina Grosse House) Also less crowed than other beaches in NYC.
For oysters & libations. The comprehensive oyster menu changes depending on what they can get that's fresh. If you know anything about oysters or just plain like them, this is without question the spot. Currently my favorite oyster (not always on their menu) is the Skookum.
The rooftop garden at the Metropolitan Museum of Art. The museum floors below are a maze of tremendous art and inspiration, and taking the elevator to the rooftop garden is the icing on the cake. 360' views of verdant green Central Park bordered by cool glass and steel of Manhattan's cityscape in the distance.