San Diego: Sushi. You might as well, since you won't be doing it again until the east coast :)
California and Arizona: Authentic Mexican. Look for places that serve a largely Hispanic clientele. If they offer menudo on weekends that's another good sign of authenticity, though unless you like tripe I wouldn't recommend actually ordering it. In CA and AZ, there's a fast food chain along these lines called Filiberto's that completely rocks.
New Mexico: Same as CA/AZ except there's no Filiberto's. But no matter: if the menu above the cash register is yellow with green letters, you're golden. I don't know why that's the case, but it's been the case in all the great short order spots I've found. Maybe the menu boards all get ordered from the same place.
Texas: Unfortunately, outside of border towns like Del Rio or especially El Paso, the Mexican food you'll generally find is likely to be no different from the Americanized version of this cuisine you'd find anywhere else in the country. Sad but true. So, switch to chili with cornbread: it's something that I'm finding almost all Texas restaurants take pride in, and it's delicious. In fact I'm hoping that one of these towns happens to have some kind of chili cookoff or contest while I'm passing through.
So, there you go: my frank advice on restaurants for the first half of the ACA Southern Tier.