My favorite barber for years here in Nogales just moved to RP a couple weeks ago and is working at Barberia de Luis at Juan de la Barrera & Melchor O'Campo. Ask for Chris, he is a great barber and speaks very good English. I can direct message his cell# in case you need more info. Highly recommended, I was pretty bummed when he told me he was moving.
I think the barber shop changed locations recently so I couldn't see it on Google Street but I sent him a text (whatsapp) and he said he is going to send me the exact location.