Nothing is more quintessentially New York than a diner. This eatery not only serves excellent, traditional diner fare, but does so in an eclectic environment that mixes Baroque decadence with Midtown grit.
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 love sneaking over here in the middle of the day to see a movie - they always have the best selection of films. I recently saw Pina in 3D and The Kid with a Bike here, and another time I saw Bela Fleck play the banjo after a screening of Throw Down Your Heart.