Ron L.
Yelp
There are a few places that every California resident should visit: Coloma, where gold was first found. The Golden Gate Bridge, both the most beautiful major bridge in the world and an engineering feat. The Earthquake Trail, Point Reyes, showing the 100-year-old effects of the 1906 shaker. And the State Capitol.
The museum is part of the actual capitol, so don't think that you're seeing only an example of the real thing. Nope, along with the county exhibits, statue of Columbus, and pictures of current Assembly members, you also see portraits of each governor, the Gov's office doors, and a second-story view of the Assembly Hall. And that's just the self-guided tour. The actual tour gives you more, but my family took that tour eight years ago and I don't remember it enough to write details here. But this is the real thing. I do remember the tour guide saying that the Governator (Schwarzenegger) sometimes came out to sign autographs.
Our self-guided tour was spur-of-the-moment, and I am not a spur-of-the-moment guy. But because our drive from I-5 to some Midtown clothing stores would take us within 1-2 blocks of the Capitol, I took a detour to Capitol Ave so the girl could see it. This became a photo op, which turned into us entering the N Street Pavilion, going through security, and seeing it for herself. The sight of her looking up to the top of the rotunda and saying "wow" will stay with me for a while. As of this writing, she's in 6th grade, so she appreciates the significance of this building more now than she would have even two years ago.
The California State Capitol. Good for school groups, family outings, or political or history buffs. Or you can sit outside under one of the yuge trees and have a nice picnic to escape the hundred-degree summer heat. Whatever. If you live here, or even if you're a tourist, just GO.