I live in Austin and I'm getting started back into trad bowhunting.
There are no shops that focus on trad, but you can buy some stuff at Cabela's or some of the big box stores for reapirs and emergencies. KC's Outdoors will make you arrows to your specs. Bob Sarrels (custom bows) is just south of the city limits and rubydog (custom arrows) is just east of San Antonio, not to far for an afternoon drive.
Archery Country in North Austin (pro-shop for compounds) has a 20 yard indoor range for $7 an hour. A trad-only league shoots there every Tuesday at 6:30pm, very informal and friendly, just show up and shoot. Fun group, nice people.
Austin Archery club has a 90 acre outdoor facility that has field archery and a 3-D walk-around course with 3-D tournaments once a month. It's open from dawn to dusk. Send me a PM if you want to check it out.
I hunt hogs on private land, but there are a few guys on this site who do well on public land. Most ads I see are $100 to $150 per day, some have an additional kill fee for large boars. You may get lucky and get to hunt free if you meet the right people. Having traded manual labor for hunting access, $100 is fair if all you do is show up and hunt a comfy, tripod stand with aan established feeder. I have never hunted turkey, so I cannot help you there.