I've never been to a Spanish or Tapas restaurant, mostly because I've only heard of one in my life and that was many years ago, but Tex-Mex nor Mexican are very different. A friend that had gone to the only Tapas I'd ever heard of was here in DFW area and it sounded great.
You'd probably have to find what may be rare, but area's with large Spanish immigrant populations. Can't say I've ever heard of any place like that though. Several different European country settlements (if you want to call them that) where great authentic cultural restaurants are, but those are usually hard to find unless from someone that knows of them.
When I visit San Antonio, I always stop by Mi Tierra in the Market Square. The locals don't really go there much because it's a tourist attraction, but they have some great carne guisada.
Edit: I reread your post and you're looking for tapas restaurants. I think Mi Tierra has some tapas style dishes on the menu, but not positive.