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!
I live above TriBeCa and take walks into and around this area often. It's quiet, usually on the emptier side, and hosts a few gems of restaurants including Tiny's, Takahachi, and Odeon - all on the same block of West Broadway.