Check out hostels in the area…hostels.com or hostelbooker.com will get you started. You can find rates in Manhattan and Brooklyn for usually 20 to 50 per night if you stay in a dorm style, or upwards of 100 if you get a private. Usually can’t find much better than that.
If you are okay with staying in Manhattan, check out American Dreams Hostel, it’s in midtown…run by a nice guy named Lou.
Good luck.
JK