These are the ones i know of off the top of my head. I'm sure there's plenty more.

http://www.hiddenfallsadventurepark.com/
30 Mins outside Austin

http://generalsams.com/
Huntsville Texas

http://www.brazosvalleyoffroadranch.com/
Private - Bryan, Texas

http://katemcyrocks.com/
Rock Crawling park no real trails.
Mason, Tx 3 hrs from Austin

http://www.nps.gov/bibe/index.htm
Big Bend Nat'l Park. On the Rio Grande. Most roads are not paved and many require High Clearance and 4x4.
Overland style Offroad with a few hundred miles total of roads.