Regarding Yosemite, you can find spots as there are cancellations all the time, but you have to be johnny on the spot and hit the Reserve America website several times a day. It can be done, but you have to be flexible on your time.
The drive up Hwy 1 can be a bit of a challenge, especially around Big Sur. It gets narrow and curvy. Nothing that cannot be done, but it is a challenge.
Take your time, pull off often, and try not to sweat the time factor.
If you decide not to try Yosemite, there are literally dozens of campgrounds around Mammoth lakes that rival Yosemite. Granted, you don't have the Yosemite Valley, but there are plenty of other options. Fishing, horse back riding, devils post pile, Rainbow falls, endless hiking possibilities, good food in town, free shuttle buses, nice camp grounds.
While I love Yosemite, it is a bit of a zoo. Tour buses, crowds, overly eager rangers staring you down. If you have a dog, expect to get a lecture about leashes, potty bags, yadda yadda yadda. It's frankly overdone, but just the same, beautiful.