I had been living in Brooklyn Heights for some time and Long Island Restaurant has been closed for as long as I could remember. Then one day, the sign was lit up and not long after the new owners had resurrected the spot with the promise to the previous owners the name and sign never changes. Order "A Martini" from the menu. It's divine. As are the french fries. They're double fried.
My second-favorite outdoor-place in Manhattan. The abandoned 1.6 km rail tracks running above Chelsea down to the Meatpacking district were turned into an above-ground park. Perfectly nice place for sitting in the sun, reading, relaxing, having lunch in some green spot in the city. Nice views at the Hudson River, New Jersey, the Statue of Liberty (little small from there but still visible) and the architecture around Chelsea.
This artist-run gallery is a hub of the Brooklyn gallery scene. You'll find Bungee, a celebrated fixture, snoozing comfortably in the office and somehow oblivious to all the surrounding chaos.
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!