I love that there's a museum dedicated to American art, founded at a time when American artists were underappreciated. The exhibitions are curated with a broad but discerning eye, and the architecture is spectacular. In my experience it's typically much quieter than the obvious choices like the Met and the MoMA - although both are remarkable, there's something I love about the scale and style of the Whitney.
The Peruvian pisco sour cocktail is among my favorite aperitifs - you won't find it better than here. A lot of people know this bar which has been around for many years, what they don't know is that the dinning is actually really good. Blinis & caviar with some bubbles are the perfect way to continue after the aperitif :)
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.