I had a similar dilemma when I rotated at HJD. I ended up using a service called Manhattan Getaways (), which places people with those who are willing to have someone stay with them for short periods. It isn't cheap, but it may be your only alternative if you don't know anyone. I stayed with a very nice woman in Stuyvesant Town, a housing development which is about a 5-minute walk from HJD or 10 minutes from Bellevue (although you should try to get an HJD rotation if possible). It was $1800 but that is not bad compared to the price of staying in a hotel. The Y is also an option but not the greatest one.
Also, there's a housing message board at NYU's website that may be able to help. I can't remember the URL, but you should be able to find it with Google. People post to the board with sublets available in NYU housing (about a 10-minute walk to HJD). Activity picks up toward the fall as NYU students go on away rotations. Unfortunately I was not able to find anything that way, but it's a good idea to try because these units will be cheaper.
The best option of all is to stay with someone you know if possible, so check with all your friends as they may know someone who has a place. Good luck, and enjoy the Gramercy Park area- it's a lot of fun.