Not sure about hotels, but if you want to spend a great night at a new years eve party, check out http://newyearsplans.com/nyc-new-years.h��
You ll have to look to Long Island City for budget sized rooms, There are sevral hotels in the area that is within a 10 minute subway ride from Times Square, Check out the link below.http://www.hotels-rates.com/Long_Island_��You can also try Jersey City, NJ, which is located on the other side of the Hudson River. Its a 10 to 20 minute commute by inter-urban rail.http://travel.yahoo.com/p-hotel-477673?f��Good luck