Ex-New Yorker.
Great food, great price, better for lunch:
http://www.luparestaurant.com/
You
have to hit
Museum of
Natural History Central Park West at 79th St, you can then see central park and hit the museums on the upper east side.
The Natural History Museum is awesome, as is the Museum of Modern Art (MOMA). Central Park is always fun because there's always something going on and someone playing music somewhere. I forget where it is, but Sammy's Noodle Bar has great soups and noodles. I think it's right on the edge of the east village. A trip up the Hudson to see some of the smaller, quainter towns is something people usually like to do. A short trip down Route 17B I believe will land you right next to the Delaware River and some incredible scenery, with rafting and kayaking all available at a lot of spots. Water is great now too. Warm enough to swim and crystal clear.
My home of Long Island has some nice spots too. There are a few towns on the north shore like Huntington that are always jumping and have great bar scenes. The south shore has the best beaches with some decent surfing. I recommend Jones Beach and Smith's Point. My two favorites. Further east on the north fork of the island there's a shitload of vinyards that will offer tours and tastings and the like. Plus who knows what festival will be going on in the city when you get here. The south fork of the island has the Hamptons. In the summer it's a great bar/club spot. If you're here on a Sunday I'd recommend going to the Boardy Barn. It's an experience, and
everyone there is looking to hook up. Then there are several beach bars you can go to on the shore itself. 7 is a nice spot in the Hamptons, as is Foggy Goggle.
Your best bet is to hook up with someone your first night here and have them show you the town. Nothing better than a local guide, and despite the rumors there's no shortage of nice people in the city or the island.