Are you considering hostels? I never stayed in one so I can't vouch for any. Looked up a few last night just to see their respective rates and locations.
I'm not sure what areas in NYC you would be comfortable or what constitutes comfort for you as you stated you wanted something more comfortable then the midtown Y.
I was thinking you spread your search away from the middle of Manhattan where the majority of tourists head straight for and headed straight for exploitation (price and comfort wise when one considers bargain options in the city). But then again I could be dealing with a bad case of wishful thinking.