check out sanantoniodiscclub.com (san antonio disc club) and lodga.com (live oak disc golf alliance) those are the two main clubs here, and they both have well run events. saturday and sunday minis... with tuesday, wednesday, and thursday minis during the spring and summer months.
there is another club in town... alamo city disc club, but there isn't much about them around. just the pdga message board. and you can find lodga and sadc on there as well.
San Antonio is a fun place to play disc golf. You'll meet lots of cool people. Right now there are 5-6 courses in town, but that number is growing. Be sure to check out the websites that have already been mentioned.