New York City is easily one of the most expensive places to live, and rent is definitely a reflection of that. Most students find that the luxury of off-campus living is not worth the time, effort, and money. Additionally, those who do choose to live off campus often end up living very far away from campus, such as in Astoria or Brooklyn, where rent is considerably cheaper. While it may seem exciting to live like a real New Yorker in a tiny studio apartment, the commute is exhausting, and the vast majority of students chooses the security and relative cheapness of campus housing.
For students who find themselves with summer internships in the city, subletting is often a good option. Lots of people leave the city in the summer and are willing to lease you their space for a few months on the cheap. Good luck finding something, though. Usually you have to know someone who knows someone in order to find a place, and most appealing offers get snatched up in an instant.