Of course the state parks, but also:
LCRA parks along the river, and Lake Bastrop are nice. The Army Corps of Engineers parks at Lakes in the area, such as Canyon Lake or Lake Somerville.
Buescher state park is nice and quiet with a fishing lake and good hiking.
There's parks around Lake Georgetown.
There's some nice parks around Granger Lake.
There's some county parks on Canyon lake Luke Potters Creek that are nice, too.