I'm surprised no one's mentioned Astor Place near 8th and Broadway. I used to go there all the time. They have a ton of stylists, though, I don't remember the name of the guy I used, other than he's Russian. Don't let pictures in front scare you into thinking they're going to shave a Yankees logo into the back of your head (or I guess it should be Mets logo now). I mean, they will do that if you ask, but the people I've seen are quite capable of "professional" hair cuts as well. I remember a Russian lady named Clarissa as often recommended. If you're older, however, you'll probably feel out of place.
Unfortunately, as I have less hair to cut these days, the barber shop at Port Authority now suits my needs.