Really depends on what you're looking to do. It's all going to be about the same cost-wise. Below is very, very high level ways of thinking about it.
- Closer to Central Park will be more residential and that's where the museums are. Less congested. Talking Upper East and West sides.
- Midtown/Times Square area will be more touristy. More commercial. Still lots to do and see just less neighborhoody.
- Toward Lower Manhattan is the hipper areas, generally. Greenwich, Little Italy, Soho/Noho, etc. Vibrant but not as gritty as, say the Lower East Side.
- Last I was in NYC I stayed in the Bowery/Lower East Side as I found a hotel cost that was ever so slightly cheaper than other areas. Even walked all the way to Greenwich Village one night. Close to Chinatown/Little Italy. Would do again.
- Unless you're working, generally wouldn't stay below, say, Canal Street. Generally.
And yeah, I mean you're going to be in the ballpark of a subway station anywhere in Manhattan you'd want to stay, so cost is usually what drives my decisions in the ballpark of where I want to stay