So, your options will be (I'm sure I'm leaving something out)
Tx Precision Matches at CCC holds a monthly Centerfire and Rimfire match. Prentice Wink runs one of the best/biggest Regional Clubs in the country. Something like 5 or more regular shooters there have gone on to win at least one 2 day national match. IMO, a lot of that is due to Prentice not making the course overly hard every month, which allows shooters to develop their skills properly.
Anderson Outlaw has a monthly match. It's limited to less shooters and is generally purposely harder to simulate more of the difficulty of a 2 day national match. This is where guys tend to start going after they are doing well at the Tx Precision matches. The difference in skill levels works out very well between the two matches.
Sotex PRS club generally hosts a monthly match. They alternate locations of Rifles Only (Kingsville), Diesel Deer Ranch (Benavides), and DEA (Dancing Elk, in Mathis).
Alamo Precision Rifle Club hosts a monthly centerfire match that is near Pearsall
Texas Topshots Precision Rifle Range seems to be doing some centerfire and rimfire matches. They are new, so don't know much about them.
Doc's is a monthly belly match near Corpus.
You can find a lot of these on the "Sotex Knitting Club" Facebook page. Or you can PM me if you would like contact info for any of the above.