Coney Island is the best for everything - the beach, the rides, the beer - but mostly for the Skee Ball. It's incredibly addicting, affordable and satisfying (depending on your aim).
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.
Best pizza in NY. Be prepared to wait. Check to see if they are shut down by the health department or tax collectors before going. Get the square pie with pepperoni and hot peppers.