Hotel rooms in New York City are generally pricy, and space is limited; so early booking is strongly advised.
Recommended options near to NYU/The New School
Washington Square Hotel, Waverly Place, two blocks from NYU/New School: http://washingtonsquarehotel.com/
Heritage Hotel , West 25th Street: http://heritagehotelnyc.com/
Maritime Hotel, West 16th Street: http://www.themaritimehotel.com/
For a wider range of options, prices and locations further afield than the Greenwich Village area, sites such as Expedia and Hotels.com are suggested. Booking.com offers daily specials on some hotels, and these beat the price of a reservation made directly with those hotels. Air BnB also has a range of listings within walking distance of NYU/The New School, and beyond: https://www.airbnb.com