It’s pretty hard to find anything cheap in Manhattan. However, I recently was on W. 96th street & Broadway and noticed a couple of hotels around there. One of them was a Days Inn (on 94th street). Their prices are considerably lower than you would pay in midtown.
This location is right on the #1 subway line, only a few stops from midtown, and a perfectly nice residential neighborhood.
Other than that, you might have to look at New Jersey if you want to save money.
Do yourself a favor and read this article, it is all about booking a hotel during the holidays and gives money saving tips on how to get the most for your money: http://www.examiner.com/x-18067-NY-Budget-Hotel-Travel-Examiner~y2009m7d23-The-Holidays-2009-in-New-York-City