What are you in NY for? Business? Sightseeing? What area are you mainly going to be in? I ask b/c if you are going to be in a certain area mostly, but stay far away from that area, you might end up paying more in taxi fare or metro fares anyway. It depends.
See-US "hostels" are not the same as they are in Europe and other countries. Usually hostels are not good places here. Your best bet is going for an economy hotel.
The Upper East side is usually the most expensive part of town-but if you say there are hostels there-which I doubt there are, but if you say so-that would be the ONLY part of town I would stay in a hostel.
Really, most of Manhattan is safe. I walk the whole city by myself at night and have never had a problem ever. It is good to look like you know where you are going, though.
Midtown, again, safe. That's the most central part of town. You are in between uptown and the Village- not far from shopping, popular tourism sights, Broadway, and not far from downtown. Midtown is the upper 20th streets-to the 50s (Broadway, Times Square). Greenwich Village is considered about 16th street all the way down to the end-that is downtown. Uptown-the Upper East Side, and Upper west side is the 50s up to the 90s. Above the 90s, you are getting into Harlem and the Bronx-stay away from there! Forget Murray Hill, theres nothing great there.
I found one listing for a hostel on west 95 th stree-which by the way is a lousy area-and the reviews were terrible. Bugs, bad service, just not good reviews. The name of it was Continental Hostel. I went to Trip Advisor .com. I didn't see any other listings for hostels in NYC.
I found a Super 8 motel-which is typically the cheapest of US motel/hotels, on 49th street, which is times square. It was for 140 US dollars per night. I doubt you will find anything cheaper in nyc. It also depends on when you are going. When will you be here?
Well, I hope this helps a little. I hope you find something-hope I wasn't too negative, but I figured it would be better for me to be realistic to you.<img src="i/expressions/face-icon-small-smile.gif" border="0"> Let me know if you have any more questions-my hubby and I work in nyc and are there all the time, very familiar with the city.