Bastrop State Park is nice. It and the adjoining Buescher State Park are located just east of Bastrop and north of Smithville. I don't know whether the more primitive camping sites are still available after the wildfire that consumed most of the pine forest a few years ago, but there are some very nice cabins there that apparently survived the fire.
Pedernales Falls is indeed a nice choice.
Inks Lake State Park is a really pretty place and has a unique appearance due to all the red rock around there. It's near Burnet.
I'd also recommend McKinney Falls State Park, which is located south of Austin and just west of U.S. 183 and Austin-Bergstrom International Airport.