There are quite a few excellent golf tours around Texas that are designed for amateurs or for golfers who want to play for money but at their own skill levels.
One of those is actually a national tour, the Michelob Ultra Golf Tour. The MUGT currently has tournament schedules in about 40 cities nationwide. It also has three tours in Texas areas: Houston, Dallas-Fort Worth and Austin-San Antonio.
MUGT events are divided into five flights based on the golfers' skill levels. You don't have to be particularly good to play an MUGT event (unless you're hoping to get into the best flight, of course), but you do have to have a love of competition and an eagerness to get some experience in tournament golf.
If you've ever thought of dipping your toes in tournament golf, check out the MUGT. You can navigate to the websites of the three Texas MUGT tours from this page.