Just FYI, Yosemite is quite a ways away. You'll need a car (plus camping gear more than likely) and 3+ hours to get there. IMO you don't have time for that if you want to do other things as it's probably only worthwhile to go there if you spend 2-5 days there.
But yes, all the museums seem right up your alley. If you go to golden gate park, there are 2 museums across from each other. The DeYoung museum (art) and the California Academy of Science (nature, imax, etc.) both are great. The Legion of Honor is also great as is the MoMA but I want to say the MoMA is closed for renovations and only has a smaller, temporary location up (you may want to look his up, I'm not sure).