The Owl Cafe in San Antonio, NM, is legendary. Home of the original green chile cheeseburger. I’ve been there a couple of times when visiting the Bosque del Apache National Wildlife Refuge.
The Owl has been around since the early 1940s. All the scientists and engineers from the Manhattan Project who went Trinity Site, all had dinner at The Owl the night before the atomic bomb was detonated.
The Buckhorn Tavern, also in San Antonio, just catty corner from the Owl Cafe on the main drag (San Antonio is a tiny town so the Main Street is only a couple of blocks long.) , also has a killer green chile cheeseburger that a lot people like better than The Owl’s. My opinion–you can’t go wrong with either one.
There’s second location of The Owl Cafe in Albuquerque. Not nearly as good as the original. (And not owned by the same people as the original Owl Cafe.)