Go do it, it's worthwhile of a week-long summer trip. Fly into SF and drive over to Yosemite/Kings Canyon/Sequoia for a few days, and then drive back to the coast (maybe San Luis Obispo area) and drive back up along the 1 through Big Sur to SF before flying home. You likely can't fit in Shasta/Redwoods unless you prioritize that over the Yosemite area or take a 2 week trip.

Just know the water is freezing all along the CA coast basically all times of the year.