This museum is often overlooked by visitors to SF, which is a real pity because it has so much to offer, and is right across the street from the Lake Merritt BART station. As the name suggests, it is THE museum of CA, and as such, will give you a capsulized look at CA history, geography, art and culture all in one setting.
Right now they have 2 special exhibits going on until mid August. The first is "Behind the Magic: 50 years of Disneyland" which was great fun. There are original sketches and scale models of the park and rides, a display on how audioanimatronics works, and even the original Mr. Lincoln from the NY World's Fair, stripped down to show his inner robotic workings! We spent hours checking that one out. There's also an exhibit in honor of the 100th anniversary of the "06 quake and fire, where you can even ride an earthquake simulator.
The museum also has lovely gardens and a nice restaurant, although you would also be close to the resturants of Old Oakland and Jack London Square as well.
Their website is museumca.org. Check it out! Be advised it's closed on Mondays and Tuesdays.