Howdy, fellow Austinite!
Instead of listing them all off, I'll provide you with a (fairly recent and correct) link of public ranges in and around the Austin area.
Click here.Now, the warnings!
Hill Country Rifle Range: The guy that runs it (Richard) is a bit....eccentric. Some people just get it out in the open and call him downright nuts
Texas Tactical has shoots there every month, although I don't know the schedule. I went there alone once. Once.
The sucky part about it is he's VERY liberal with his range rules. NFA friendly, and he even has pistol steel to shoot at.
Austin Skeet Range: I LOVE the skeet course they have. They have high and low skeet houses, and the course is pretty neat. That being said, I've heard tales (but not seen firsthand) of the bullet holes in the benches and such on the rifle range. It has a reputation in some circles of not being the safest place to shoot rifle/pistol.
Now, some personal recommendations:
Tony's Guns and Range up on 183, near Florence. He really doesn't care WHAT you do, as long as you hit the berm with your shots. Pretty easy to do.
Austin Rifle Club: If you wanna join a club, with a REALLY nice range, go here. You have to apply for membership, and there are annual dues. The range is NICE with a capital N. They're NOT NFA friendly, however (for MGs at least). If you're interested in this one, contact me. I can bring you along as a guest on a shoot, and you can see if the range is to you're liking. Check their webpate (listed on the page I listed above)
T.I.G.E.R. Valley in Waco: Official site of Gunstock! I don't know (I don't think you can) if you can just go up there for the day. But if you ever get the chance to take a course here, DO IT. The guys out there are some of the Finest People you'll ever meet and shoot with.
There you go! If I can be of any further assistance, let me know. And I'm serious about the Austin Rifle Club guest shoot offer. Just contact me if you're interested, and I'm sure we can work something out!
-Gloftoe
(edited to correct spelling for my local SpellingNazi)