Texas State Capitol
I remember once about 20 years ago, before 911, I went to the Texas State Capitol and could walk around inside well into the night. The interior office doors were closed, but you could visit the rotunda and admire the architecture of the stately building.
I've been to Austin several times since then, but hadn't stopped there for a visit. Last month, we made an unplanned stop and had to settle for an exterior walk-around. That was fine though, since there is still lots to see outside and it gives me an excuse to go back soon.