Lots of great suggestions. I don’t know LA well. So, I’ll stick to the Bay Area. On the way down to LA, Big Sur is pretty cool as are Carmel/Monterrey. One can find Airbnbs in both places, but you might need to book somewhat in advance.
With respect to SF, @mathmom, I think the thing is to never leave anything visible in the car. If you do, there is a high chance your windows will be broken. Probably somewhat safer in the trunk. But parking in SF is expensive so it might be better just to take ubers and BART within the city.
ShawWife and I lived in Sausalito for a while and love it there. The bike ride across the GG Bridge and lunch in Sausalito is a great adventure and would be something I would do, but our interests are probably 1) outdoors; 2) art (ShawWife is an artist); and 3) food. There are spectacular restaurants in both SF and LA. In SF, I really like Marlena (a husband and wife who worked at separate Michelin star restaurants and formed their own which also has a star). Price was very reasonable given the quality when I was there (maybe a year ago). But, there is wonderful Asian/Asian fusion food. I been a few times to a Vietnamese restaurant named Lily’s – the owner is a character. One of my favorites is Sushi Ran in Sausalito (the owner is a great guy) but this one would be expensive. (For LA, isn’t the world’s best taco truck supposed to be in LA?)
SFMOMA can have great shows. The De Young Museum is beautiful. There are a couple of private galleries that impressed me. Todd Hosfelt Gallery, which was edgy and very interesting, although a little bit snooty. Berggruen Gallery is like a museum.
Yosemite is spectacular. I proposed to my wife on top of Half Dome (and ShawSon proposed to his wife on top of Yosemite Falls) so we have a sentimental attachment as well. However, it seems pretty far away if you only have six days. Hiking in Mt. Tam can be very nice – views of the ocean and the bay. I believe you can mountain bike there as well.
Driving in the Berkeley Hills or visiting the Stanford campus could be fun – my first time driving up Palm Drive to Stanford was actually a moving experience.
In LA, I liked the beach volleyball in Hermosa, Redondo and Manhattan beaches, I think. Venice beach is just fun. In both cases, my last visit was maybe a decade ago.
There are a few Frank Gehry buildings in LA including his house, which I think is in Santa Monica (could be Venice). The Disney concert hall is iconic. https://blogs.getty.edu/iris/10-frank-gehry-buildings-to-see-in-l-a/.