You can't come to Austin and not see the Capitol building.
The architecture is great, both inside and out. The grounds are nice too.
Take the time to join a (free!) tour once your inside. The guides are really friendly and informative.
If you're not up to date with your Texan history, visit the Bob Bullock Texas History Museum before you go - it'll make the tour that much more interesting because you'll really know what they're talking about.
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