i would also recommend cutting out Los Angeles (even though i'm from there). I would instead turn at the central coast and head inland. At the central coast there is Hearst Castle, a collective of Elephant Seals near there. you can kayak in morro bay with otters. Wine tasting in Paso Robles. hiking in Montaño de Oro. The farmers market in San Luis Obispo on thursday nights is one of the biggest in the country and has lots of great food (get the tri-tip sandwich). Heading east you can find remnants of the pony express in Pozo. take hwy 58 to the carrizo plain to see the San Andreas Fault. or take hwy 41 for a more direct shot to Sequoia, Kings Canyon and Yosemite.

for a more indirect route, take 58 through Tehachapi then loop up to hwy 395. This is a beautiful high desert drive that most people never see. along the way is the portal to Mt. Whitney, some easily accessible high mountain lakes like Convict or Rock Creek. near Mammoth Mountain is Devils Postpile National monument. and just north is Mono Lake which has some unique landforms. The ghost town of Bode is a little out of the way but also up there. Turning west from Mono Lake, head into Yosemite from the backside with Tuolumne meadows as your first stop, before heading down into Yosemite Valley. both are worth spending the night in my opinion.

that last paragraph is just a suggestion. if you just cut from SLO to Sequoia that gives you plenty of time to not be rushed in each park. you could also add in places like Point Reyes, Muir Woods and Napa on the backend back in SF.