I was a tourist in my own city, exploring the state Capitol. It was actually very cool! There is a great walking tour that takes you through several floors of the building, or you can follow a docent. The details in the hardware and glass are simply beautiful. And of course, the rotunda is epic. Count how many Texas stars you see (hint: there are probably thousands)!
My advice for visiting: use an entrance other than the main (south) one. There are entrances on all sides. You have to go through a metal detector, so the line backs up at the front.