I like the rock garden and accompanying display outside the Berkeley geology building -- where else are there exhibits on rock types or on geological processes?
Alas, you live in the wrong era. In the 1960s and 1970s by far the best and most informative was the geological museum in South Kensington (West London). Sadly, it is now dumbed-down - sacrificed on the alter of children's populism. The Colorado School of Mines geology museum is reckoned to one of the best, especially for minerals. Otherwise, I can't speak for America, but if you are ever in Vienna you must visit their Natural History Museum where the mineralogy and meteorite galleries are gob-smacking superb. The Natural History Museum in Adelaide, South Australia has the world's best exhibit of Eocambrian fauna, and also boasts a spectacular opalized plesiosaur.
Since you asked about California, I'd have to nominate the La Brea Tar Pits and Museum, even though I've never been there. It's hard to imagine a better teaching/learning tool than an actual fossil trap.