In San Antonio if you are looking for an alternative to Tex-Mex, try a German restaurant. There is a surprisingly strong German restaurant presence, largely, I believe, because of the immigration in the late 19th century.
Having said that, I have no personal rec’s. The only time I was in San Antonio (a while ago) I did not eat at any German restaurants. The only Tex-Mex place that I recall is Mi Tierra. It has been a while but I remember liking the restaurant and also that they had a nice bakery.