Welcome! I live in South Austin too. In my opinion, the best range is Hill Country Rifle Range. But the owner, Richard, (aka Crazy Richard) is a few short of a six pack, if you catch my drift. He's a racist, anti-Jew, government conspiracy wacko. BUT THE RANGE IS GOOD! I go there to shoot and not to socialize with the wacko. The rifle range has covered concrete benches, and goes out to 400m. Steel targets at 300-400m, paper targets at 100 and 200m. The pistol range is 25yds with steel targets, but no cover, so it gets hot pretty quick. There is some type of action pistol club that meets there on the weekend, once or twice a month, but I don't have any details except those folks are real friendly and are always looking for newcomers.
Red's indoor range (100yds) is also another good place to go on the South end of town, if you don't want to drive out to HCRR.
Let me know when you want to go! I'll be happy to show you around!
Dave Peacher