If you are willing to drive a ways out of town, you can visit Hamilton's Pool--off 71 West of Austin on Hamilton's Pool Road. It is a natural cave whose top fell in at some point and it is now a waterfall and swimming hole.
There are some beautiful lakes close to Austin where they often hold concerts (The Backyard) Morissey and my favourite David Bowie have performed here.
There are so many area lakes, rivers and creeks. Get outside and enjoy! The picture in this photo is of Reimer's Ranch at sunset on the Pedernales River.