Lee T.
Yelp
I go here for two reasons: I take my granddaughter here (as others have mentioned, it's a great quick stop for kids) and a geology hiking group I lead.
Others have given good details, but one other tip I'll add: While the building is officially closed on Sundays, I've never not been able to get in. Two ways in when closed: Wait around for 5-10 minutes and you will likely find a grad student coming out who you can sneak in behind (especially if you have young kids in tow) OR (I worry about posting this, hope they don't fix this) if you pull on the doors without handles (the doors are in pairs, the right one has a handle, the left does not), you can usually find one that has not latched completely, and in you go!
UCB, and most universities, have many great "hallway museums" (check out the rocks in the halls of the Earth and Planetary Science Department), and the dinosaurs in the hallway are a great example. They also have a cast of "Lucy" that can be viewed.