I can't help with camping information, but I think Austin and surrounding areas are great,  A couple of "must sees" in the Austin area are Luchenbach, and the LBJ ranch.

Luchenbach is more than a country song.  It is a tiny town with a small country store/post office that sells beer and has picnic tables under live oak trees.  Nearly any afternoon there will be someone playing a guitar, banjo, washboard or something and people sit under the trees and listen.  Time stands still.

The LBJ ranch is for guys like me that recall the former president.  The property is much like it was when he lived there, and he is buried on the grounds.