Are you just coming as a tourist? If so, then you probably have more flexibility. I haven't done a lot of looking into hotel/hostels (y'know, since I live here and all), but I just booked a room for someone at work, and I can tell you the rates are a good 2-3 times more than any other part of the country. Look out for the hospitality tax, too, since that's pretty steep. (I don't know the exact number, but it's in the 10-15% range.)
If you're on a budget, you might want to look into the other boroughs. It's pretty easy to get from Queens or Brooklyn to Manhattan, as long as your hotel/hostel is near a subway stop. (Parts of Brooklyn are pretty up-and-coming, so you can definitely spend a day or two playing tourist there.) Places on the New Jersey are more affordable, and the taxes are lower, but transportation is harder since they're not on the same MTA transit system. (There are trains, but then you'll have to buy your train tickets as well as your subway tickets.)
If you're really in a pinch, you could try airbnb, where you can rent out people's spare rooms. I haven't tried it, so I won't vouch for it, but it's an option.