Are you military? Camp Bullis and Fort Sam Houston both have decent outdoor ranges and Bullis holds a monthly 3D shoot, although I’m ashamed to say I’ve never been
The monthly Bullis shoot is a little underwhelming, but the static range is nice. Morrell bags out to 60 and a covered shooting line. When I was at the Total Archery Challenge this year, someone mentioned a monthly 3D up north of town, you might call Leading Edge Archery in Boerne to see if they know. I think there are monthly shoots in Fredericksburg as well. I shoot the Austiin Archery Club monthly shoots, but they're a little further from you.
If you've got base access, Bullis also does deer, turkey, and hog hunting. You've got to deal with military hunting rules, but they've got lots of animals and no lease fees.
Lone Star Handgun on the East side of town has a big archery range. I have only shot my firearms there though. I normally just shoot the 20 yard at Mesquite archery. Welcome to town