Mexican food that is borderline TexMex...
The answer is probably not really. If you are craving food you might get in Santa Fe, you will only get a poor imitation of that at the few places here that try to do it. We have things we do quite well in Chicago, but that style of food isn't one of them, and it is likely that you will be disappointed because your expectations will not be met.
When coming here, or anywhere, really, it's best to try to experience what that place does best, and not try to recreate what another place does best.
2 words. Uncle Julio's.
They are part of the Uncle Julio's chain in Dallas, which I have not been to. However, they are also a spot on duplicate of Pappasito's in Austin and Houston, which to me is quintessential Tex-Mex.
Very good fajitas, and solid enchilada platters. Solid guacamole. Soft tacos are made with flour tortillas as opposed to corn (that's a big distinction I find between Tex-Mex, and "real" Mex). Guacamole is fine as well. As is the chips and salsa, and the queso.
Tex-Mex: As in food that has originated in style from Texas & the Southwest regions of the US, NOT Mexico. And unless you refer to it as I do at time as Old Spain or Old Mexico it has little in common with the food of Mexico proper.
The food is typically very spicy, using flour tortillas & corn, sometimes the food is "smothered" in either a Nacho type of processed cheese or a red or green chile. Tex-Mex food has given us fajita, Nachos, red & green chile tamales and Frito pies, yummy!
Sadly, your not going to find any of that great stuff here, most of our fare is very Mexican provincial and is more representative of the recent wave of Mexican immigrants that have predominantly come here from Mexico City, Durango and Tuluca. Sure there are other area immigrants of course, but the big numbers are mainly from these areas, and the food & restaurants reflect that.
The only thing I can think of that offers something close to this fare is the chain "On the Border", and they do a horrible job of representing.
Try Lalo's & Pepe's (which I prefer), they may be a better match to your exact request.
Otherwise go authentic and live a little!! LaPasadita for example.
Well, there are a ton of neighborhood Mexican places with great guacamole and fantastic tacos that don't serve mole (or at least they don't specialize in mole)...but I wouldn't call them TexMex.
Most of the Mexican food in Chicago tends to replicate "typical" food in Mexico and is probably what you're looking for, but by virtue of the fact that most typical Mexican restaurants in Chicago are made by and for Mexicans, I hesitate to call it TexMex because I assume that the cooks are eschewing Texan influence. I don't know: I guess the term "TexMex" throws me off a bit. I think that for me, what distinguishes the Mexican food in Chicago from what I think of as TexMex is that most restaurants use a white chihuahua cheese instead of cheddar (if they are using cheese at all), they use more cilantro, they have more soft tacos rather than crispy. I'm sure other people can name other differences, but those are the ones that come to mind as major ones.
Are you distinguishing TexMex (ie: guacamole, tacos, burritos with steak, chicken, pork, combination platters etc) from something like Rick Bayless's restaurants? There are probably hundreds of restaurants that fit that bill (typical restaurants, that is).
As far as where to go: that depends on where you will be staying and where you are willing to go. There are plenty of threads on this board that cover the Mexican restaurant scene.