I second the motion. As long as you're in town, definitely go to Zilker Park and Barton Springs, if not to swim (the water can be chilly), at least to check it out. The Taniguchi Japanese Gardens are also located there. If you're in the mood for some exercise, they have canoes for rent that you can paddle out onto Town Lake. There is also a miniature train ride for the kids.
Also, if you like books, there is an excellent "non-chain" bookstore called Book People with a large selection at Lamar and either 5th or 6th Street.


Further suggestions:
1.Stop in New Braunfels on the way and check out Landa Park (a city park with a beautiful lake, cypress trees and a miniature train foir the kids). Nice spot for a picnic. There is a great waterpark in New Braunfels (The Schlitterbahn), but on Labor Day weekend it will be such a zoo that I would recommend avoiding that area entirely. Also, you might like the town of Gruene (pronounced "Green"), just north of New Braunfels, about 5 minutes off the interstate, take the Canyon Lake exit. Kind of touristy, but has a Texas flavor and fun for a quick look.

2.Stop in San Marcos and take a glass bottom boat ride on the San Marcos River at Aquarena Springs. http://www.continuing-ed.swt.edu/aquarena/

3.Try authentic Hill Country barbecue in a unique rural setting at The Salt Lick restaurant, outside of Austin about 25 minutes, near Driftwood.
The best time to go on weekends is at lunch or during the afternoon. Dinner is usually so crowded that it can spoil the experience.
http://www.saltlickbbq.com/