The Washington Square Hotel is relatively reasonable and very convenient to NYU. When reserving by phone (212-777-9515) you may be able to get a discount by telling them you are attending an event at New York University.
Another good choice is Club Quarters, whose World Trade Center and Times Square locations are a short subway ride from NYU. When reserving by phone (203-905-2100), ask whether there is a special rate since you are attending an event at New York University.
A list of "preferred hotels" is available at this website. Some (but not all) the hotels listed there offer special rates or discounts for guests who are booking to attend an event at New York University.
January is a relatively low season for hotel rates in New York, so a search engine like Expedia may offer good options.