There is a location of the El Paso restaurant Carlos & Mickey's IN the terminal! It is very popular in ELP. Also, my favorite enchiladas are in the strangest location very near the airport: a place called Gerardo's at the LaQuinta on Montana St. Best cheese enchiladas I've ever had, New Mexican style. They may have changed the name recently, but it's still the same food.
Where did you end up eating?
Some good places were recommended to me here:
Of these, Rainbow Fountain is quite near the airport, and one of the branches of Burritos Crisóstomo isn't too far away. Valentine Kitchen is on the other side of town, but boy, was it good.