I love Austin! It’s one of my favorite cities I’ve ever gotten to visit. I recommend the downtown area, right near the capital. It’s very easy to walk around in, with wide sidewalks and beautiful views.
As far as specifics, I enjoyed the Mexic-Arte Museum a lot. I also found their gift shop to be a treasure trove of very reasonably-priced suitcase-stuffers I still use and admire today. Of course I have quite eclectic tastes, and I’m sure Mexican Art isn’t for everyone, but there are a lot of museums and other tourist attractions within walking distance of the capital.
I also recommend Roy’s (“Roy” himself was on Iron Chef America, swoon). It’s Hawaiian food – authentic, not just throw a pineapple on something, and call it “island flavor”. It was a bit pricey but absolutely delicious.
Have fun!! I’m jealous of you!