There is the New York University (NYU), it's the only one I know, but I live in France, that's normal ! I know 12 out of 20 is enough to go there + money of course. http://www.nyu.edu/
The best college in NYC is Columbia. It's an Ivy League school. There are a lot of Ivy League schools in the northeast area of the US. The tuition costs a lot though...
There are plenty of other regular colleges. NYU is a pretty good school