NYU doesn't exactly have dorms but they do offer on-campus housing in apartment buildings.As far as top 14 schools - I know Michigan has the Lawyer's Club which is their ls dorm. And doesn't Harvard have dorms?
The housing at NYU is pretty nice.As the earlier poster said they are actually renovated apartments.For the undergrad housing you had to pay extra if you wanted to stay during the summer, but it was definitely do-able.
You can use your student loans to pay for housing. At NYU, however, I think you have to send in a housing deposit along with your tuition deposit, which is before most people get their loans.