Austin City Hall is located right across Vic Mathias Shores. It's architecture and size separate this building from the massive developments around it. Don't be afraid to walk in as it is community friendly. You can do so from 8 to 5 Monday through Friday.
You can schedule a Tour before visiting or you can just walk in. Why would kids have any business in City Hall you ask? The first answer is The People's Gallery.
The People's Gallery is a showcase of local artists that motivate dialog, understanding and enjoyment of visual art. It is not very interactive, but it's a great opportunity to learn about sculptures, symbols and materials with kids. The best part is that it is a year round and free exhibit. Every year they add to the gallery as they have an open call for submissions from August through October.