The one (and only) thing I miss about living in Albuquerque, New Mexico is the food. "New Mexico Mexican" is different, and not easily found outside the confines of that state.
Carlsbad Tavern gets it though. They offer truly authentic New Mexican cuisine. Some will love it, some won't.
On top of good food, the atmosphere is cool too. Even on a freezing cold night (freezing from the Phoenix perspective), you can sit comfortably on the wicked cool patio thanks to fireplaces and heaters.
Service has been above average on every trip I've taken.