L.A.
Go to Barton Springs to swim
Zilker Park also has a Dinosaur Garden
Here is the schedule for the Free Outdoor Summer Musical.. It is a ton of fun. This year it is the Sound of Music
http://www.zilker.org/showinfo.html
Visit Mt. Bonnell, it is on of the highest points in Austin and is great viewing.
Visit the University of Texas.. Museums.
Eat at "the Oasis" on Lake Travis It sits on the side of a cliff.
See if the Bats are still in town, you can watch them fly out from under the Congress Avenue bridge at dusk.
Make plans to see a movie one night at the drive in movie theater.
You will need to make a reservation.. Take your own cooler and snacks.
http://bluestarlitedrivein.vbotickets.com/events
Make sure to eat at one of the food trailers on South 1st street
Get ice Cream at an "Amy's Ice cream" shop.
There are many nights you can listen to live music at different family friendly locations..
Threadgill's
Shady Grove
Spider House.
The information can be found through the 2 Austin Papers.
http://www.austin360.com/
http://www.austinchronicle.com/music/
If you are already going to be in the area.. You must, must go for a day to Schlitterbahn in New Braunsfuls.. It really is the largest Water Park in the World.. It is only about 20 minutes out of town. You can take your own cooler.. Very fun..
Let me know if you have any questions.