Safar Coiffures on 235 Newbury Street in Boston immediately comes to mind. There are a bunch on Newbury but thats the one I usually go to and I like them. Ask for Andy.
Newbury Street Hair Salon - Salon Acote on 132 Newbury Street in Boston has really great stylists and you can sip on some wine while they work your hair! Really cool staff
Revive Hair Studio on 670 Tremont Street in Boston is amazing but booked like crazy and it costs around $50 per cut. Book weeks in advance to avoid going to a crappy place when your hair needs a good cut.