I just checked out NYU's guide to off-campus housing and small apartments on Manhattan seem to start off at a crazy $1100 (I assume that's monthly). That's quite understandable though considering Manhattan's population density. I guess Staten Island or something would be more affordable.
I live in a student village (cheaper rents than private apartments) in a one-person apartment @ around 18m^2 (~194ft^2). My rent is around 250€/mo. ($320) [edit: rent includes heating, electricity and internet connection].
I could consider sharing kitchen/wc, but sharing the entire apartment with some stranger for years seems quite weird to me
