Zilker Park and the Barton Springs Pool (which is located in the park). The pool is fed by a natural spring --- so the water is the same temperature in May as it is in August or November. It is extremely refreshing.
The park is a short distance from the Congress Street bridge.
And the original Schlotsky's is (or at least was) on S. Congress.
Texas has an imposing state capital - it is the largest in the nation.
There are caverns (Inner Space Caverns) in Georgetown, TX which is between Killeen and Austin. You can also exit I35 at Georgetown and follow University Drive to my alma mater, Southwestern University, which has a beautiful campus.
In addition to the LBJ library, there is the Harry Ransom Center at the University of Texas. Within the HRC, there is one of the few remaining copies of the Guttenburg Bible. There is also the J. Frank Dobie collection. And I believe that there is a complete replica of Arthur Conan Doyle's study.
At 44th and F Street is the Elizabet Ney Museum. A very small museum of a woman sculptor from the late 1800s. A small museum which was her actual working studio.
On the west side of town there is an observatory. I am not sure that it is worth going to now that the city has grown out past it.
My favorite barbeque is at County Line --- also on the west side of town. Chuy's has great chile rellenos --- one of the few places where you can get them stuffed with picadillo (ground beef, olives, raisins and pecans).
Lots of wonderful things to do in Austin.
elaine