The newest branch of the Metropolitan Museum of Art opened in the landmark former Whitney Museum building (designed by Marcel Breuer; there's an architecture tour you can listen to on the Met's website) in 2016. Exhibits are dedicated to 20th- and 21st-century art, with sculpture, photographs, video, design and paintings from the likes of American and international figures such as Edvard Munch, Claes Oldenburg and Robert Smithson. Your three-day admission includes the main museum, and medieval exhibits at the Cloisters.
Students from CT, NY and NJ can pay as you wish. On the lower-ground floor, Flora Bar is one of the nicest museum drinking spots in New York.