I've only been to New York once, so I couldn't tell you all the nuances about NY pizza that I'm told exist-but Leon Gessi's is pretty close to that pizza joint in Manhattan.
The pizza's really good, and I like the layout of the restaurant and think the pictures create a good atmosphere. It's very enjoyable, good for a smaller group or a cheap date with a friend. The place makes you feel good when you walk out. Highly recommended-it's up there with Borriello Brothers for the food and Fargo's for the unique atmosphere.