The rooms at the Big Apple Hostel are adequate in size. Some are smaller than others but all have two bunk beds. I have stayed there many times and never felt that my body or possessions weren't safe. They have private rooms there (with shared bath) but it's much more expensive. ($125)
Also, I just looked up the rates and it looks like they've raised them a bit. For the time jeff_thedancer will be in New York a bed in a shared room is $45/night. In general the rates range from $39 (off-peak) to $60 (New Year's Eve).
I know I'm sounding shill-ish but it's my favorite place to stay in NYC because when I stay there I can afford to see more shows but I don't have to sacrifice too much in terms of location, safety, cleanliness etc.
Last summer I thought I had booked a bed at the Big Apple Hostel, got there and well, it turns out I didn't do a very good job making sure all my plans were taken care of (oops!) They were booked for the night that I arrived, so I had to stay at another hostel much farther uptown.....and well let's just say I was glad to move to the Big Apple the next day.