The Swiss guardsmen and Vatican monsignori and even the Pope's private secretary, "Il Bello," all go here:
Via Plauto, 24 (Borgo Pio S. Pietro)
It's a nice place with two young kids who cut hair there.
I was there once, but never again. A haircut is a sacred action: the barber shop is to be dumpy and the barber is to be an old guy. Those were the rules since our boyhood and my brother and I still abide by them ad perpetuum rei memoriam.