Austin is right where the hill country meets the coastal prairie. Drive south or southwest and within an hour or two you’ll find quaint little hill country towns that were settled by German immigrants, like Fredericksburg, Gruene and Boerne. Each boasts of their shopping, cute downtown centers, and bed and breakfasts. Or stay out of towns and go tubing on the Guadalupe, Comal, or Frio rivers.
You can also go hiking at Enchanted Rock, a huge granite dome about 2 hours outside of Austin. The best time to go do this is in the spring, when the bluebonnets are out. Absolutely stunning.
For larger metropoli, head an hour south to San Antonio to see the riverwalk and the Alamo. Dallas and Houston are about 3 hours away.