Today I'm searching for good barbacoa. I dined at a modern Latin/fusion restaurant miles from here and they served something they called barbacoa (tasted like mop strands soaked in mild chili sauce). Barbacoa can be done with beef cheeks and/or the meat from the head braised then flash grilled to add some crispy bits.
The decor is minimal with some paintings and decorations, people are here to eat good Mexican comfort food. The place is small and the service is quick and friendly.
They don't serve barbacoa exactly, they have cabeza (beef meat from the head of a cow). The barbacoa from my childhood was made from beef cheeks and cabeza. I sampled the cabeza taco, which was good but I would recommended going light on the condiments (onion and cilantro) to get the full flavor.