That is one cool place to check out. There is a zoo in the park even.
The bars in the village are pretty cool as is are the restaurants.
The meat packing will have some hot women and the best restaurants. Good bars and clubs too, but it can be pricey and trendy. They are not ready for teh jacket yet I think. Washington square park is also a favorite of mine too.
Central park is a must see, but its huge. I personally would recommend the Museum of Natural History. It is right next to central park on the upper west side.
Personally I am a fun of Sushi Samba. Bond Sushi. Peep Thai. Gugeenheim Musem. Museum of Modern Art. Crumbs bakery. Taking the Subway everywhere. Magnolia baker. Many lowest east side entertainment spots. Have a great time bro.