Best contemporary art museum in NY, have to take a train that goes along the Hudson river (best views during fall season!) / rent a car. This museum only uses natural light, and has pieces from Richard Serra, Judd, Sol Lewitt, Walter de Maria, Robert Smithson, Flavin, all best of the best!
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.
Fav art bookstore in the city (and the world?). Great place for inspiration and reference art, both new and vintage finds. Not very cheap but mostly quite worth it.