Here is a list of known dorms, apartments, and residences that allow students doing internships to stay in them.
Note: Most colleges and Universities in the city have housing for non-students, but ONLY during the summer months.
Best place for Subleases/Listings/Rentals:
www.villagevoice.com --Classified Ads
92nd Street Y --(FULL until Jan. 2007)
(more will be added to this list as time goes by...)