There are a handful of restaurants that could compete for the title of best Mexican food in El Paso. The Little Diner is consistently on that list, as Tha Groovin' Gourmet's review illustrates, and this seems like a good time to expand the Chow Database with information about another major contender-- the L&J Cafe.
The L&J is as famous for its location as for the food. The old building at 3622 E. Missouri, across the street from Concordia Cemetery, is actually a bar that is one of the city's most popular hangouts. The restaurant, located in back, is almost an afterthought. I believe other Mexican restaurant owners have actually visited the L&J to get ideas about how to make their places more dive-like. It's hard to do, though, unless you have an authentic 1920's era building that has gone through various stages of remodeling and expansion to accommodate the current dozen or so dining tables. If you cannot find a parking place within two blocks don't worry too much-- the cars probably belong to bar patrons and it doesn't necessarily indicate that you will get on the dreaded waiting list for a table.
Meals at the L&J start out with the complimentary chips and salsa. A puréed green chile salsa is usually served, but requesting the red one provides a more satisfying experience IMO. I would suggest sampling the flavorful rice before digging into the main meal in order to gain a full appreciation of it (Kiki's is the only other restaurant I know with a similar quality rice). Beans are strictly for providing an alkaline counter-point to the highly spicy food, but being made with vegetable oil, are more healthy than most.
A number of restaurants in El Paso have excellent red enchiladas. The ones at L&J are deep red, with enough sauce to spill onto the plate and into the other items. This is a good sign, indicating that there will be no shortage of flavor, with enough spices added to enhance the experience and leave a slight aftertaste. The red chile here is extremely hot by El Paso standards, and for that reason the enchiladas may not be the best choice for everybody, but the sauce is still somewhat subdued when compared to many of the ones served in New Mexico. If these are not the best enchiladas in El Paso, they are so close you will not go wrong with them.
The green enchiladas are in contention with the Little Diner and Chope's in La Mesa, New Mexico, as the best in the area. The ones at the L&J are somewhat soupy, and are similar to the ones served at the Little Diner, but lacking the large amounts of cheese placed on top. The green chiles used at all three restaurants are top-notch quality, with Chope's being the hottest, L&J in the middle, and Little Diner the least spicy (but still hot!).
The menu contains all the standard Mexican food items, and I believe just about everything is good. Most people, including myself, go primarily for the red enchiladas.
The homemade lemonade makes an excellent drink, but is usually only available at lunch. Drinks are also available from the bar.
From I-10 take the Copia Street exit (just west of the US 54 interchange), go one block north to Missouri, and east one block to the restaurant. Concordia Cemetery is an attraction in itself-- you can enter from the north side (on Yandell Drive), a couple of blocks north of the restaurant.