When I think of Alameda, I too think of the bridge traffic. perhaps it's better nowadays with covid. It's a lovely place, though, aside from that issue.
I assume you are driving? I think if it was me, i would start out at Davis and spend a night there to allow more time to absorb the atmosphere and give time to see the capitol building. Then I would go the Bay Area and choose a home base that is convenient to Palo Alto (stanford), your cousin, Berkeley, and San Francisco/Muir woods. From a purely practical POV, you could stay in the East Bay near 92 or 84 (bridges) and do day trips, but they themselves are very boring places lol That's near me, so I know the area well and I can help you if you choose that route. Berkeley could work, too, though it'll be a trek to Stanford.
Pleasanton and Walnut Creek can be a pain with 580 and 680 traffic, though it's definitely less nowadays.
"Friendship is born at that moment when one person says to another, "What? You, too? I thought I was the only one." C.S. Lewis