Priceline & Hotwire are good recommendations, but if you're arriving in the next 3 weeks also try www.ratestogo.com
I've used it for 2 out of my last 4 visits to New York and ended up both times in the Signature Suites near Washington Square. These are executive apartments---so the first time my friend & I ended up in a one-bedroom apartment with ensuite kitchenette. Booking with Signature Suites directly they won't let you book anything shorter than a one week stay, so they dump their shorter-term vacancies on ratestogo. It's not luxury accommodation but clean and well located.
By the way, avoid the Hudson, which is where I stayed this past weekend. In our Queen Superior room, the shower was 18 inches wide and features a glass wall through to the bedroom, perfect for the voyeur & exhibitionist in all of us.