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).
When I moved to NYC in the summer of 2009, my wife Hannah and I went straight to Central Park and the Belvedere Castle. It was the first time I fully grasped that I lived in New York and it felt euphoric standing on that hill. For me this place is still a romantic symbol and reminder of the spirit and essence of the city and the reasons I live here.