The housing situation in New York City is a bit tough. The reason is not the lack of accommodation. The problem is rather that you can’t afford these places, and even if you can, most landlords require that you have a good credit (in the United States unfortunately) and that you can prove that you earn 40 x monthly rent. You do not do that as a student. Me and my friend who moved here together realized after a while that to get our own contract for an apartment, even far from the school, would be basically impossible.
We solved our home situation through a Facebook group where people advertise about vacant spaces in their houses. We were so lucky that there were two rooms available in the same apartment, and we share it with the third girl who’s also from Sweden.
However, a monthly rent of at least $ 800 is expected, and probably more if you want to live in a pretty good area.
We live in a neighborhood in Brooklyn with about 30 min travel time to Midtown where the school is located.
A good tip is to look out for various Facebook groups for those who live in New York and sign up for the apps as SpareRoom and Roomie.