There is great camping not far from the city at Pedernales Falls State Park. Hike and bike through the falls and spend some time relaxing and bird watching.
Lockhart, Texas estimates over 250,000 come to their town to eat BBQ. Blacks, Smitty's, Kreuz serve meat unlike anything you or the other 250,000 people have eaten. And while you're looking for BBQ, drive to Llano and Elgin for some more!
Some people would say visiting Salt Lick BBQ in Driftwood is a religious experience -- meat, cole slaw and cobbler worth praying to. Bring a 12-pack of beer and make yourself comfortable, this is a meal you'll remember.
Fredericksburg is just an hour outside town and makes for a perfect getaway. You can learn some history at the Vereins Kirche Pioneer Museum and the National Museum of the Pacific War, shop for antiques and then close out the day in the wineries.
Gruene Hall is the oldest dance hall in Texas and the historic birthplace for acts like George Strait, Lyle Lovett and Robert Earl Keen. Their dance floor is always packed with music lovers basking in true Texas music waiting for you to join them.
Drive 30 miles west of Austin to Hamilton Pool to see an amazing swimming hole/cave/waterfall that was featured in the film Tree of Life. If the weather is too cold to swim, take some time to hike there instead (and stop for BBQ at Opie's on the way home).
Inner Space Cavern is just down the road in Georgetown. It's one of the biggest caves in the state and is a perfect place to spend a hot afternoon.
Just outside of town are the Texas Hill Country Wine Trails. You'll get a glimpse of some of Texas' most iconic scenery while tasting award winning wines at a number of beautiful vineyards and wineries.
Enchanted Rock is an awesome spot for hiking. The huge mountain is made entirely of pink granite, and the views at the top make it well worth the climb.
The Hill Country Flier is a steam train that takes you from Cedar Park to Burnet where you can shop, eat, and even take in a gun fight. It's amazingly, stereotypically Texan.
At Aquarena Springs in San Marcos, you can take glass-bottom boat tours. You can see hundreds of springs in action along with wildlife like soft-shell turtles and huge catfish.
Outdoorsy folks need to take a trip to Reimer's Ranch for some mountain biking or rock climbing. Located just on the outskirts of Austin, it's great terrain that makes you forget about city life.
Travel about 90 minutes south of Austin and you'll reach the heart of downtown San Antonio. Take a riverboat tour or eat and drink on the patio of one of the dozens of bars and restaurants lining the famous attraction and if you still have time, don't forget to check out the Alamo.