I'm a sucker for a good green chile cheeseburger, and really like:
The Monte Carlo Steakhouse
Blake's Lotaburger (sorry!)
the Fiesta Burger at the Frontier
the Bobcat Bite in Santa Fe
the Owl Bar and Buckhorn in San Antonio (10 miles S of Socorro)
the Outpost in Carrizoso
Bob's Burger Bowl in Santa Fe also gets really good reviews, but I have yet to try it.