If you really only have such a short time you need to pick your bit of California and stick to it. I’d agree with doing a linear trip, but it depends on your must sees. Driving into LAX for an early evening flight home is horrible and I’d do a great deal to avoid that.
Really, if it’s nature and landscape you’re after (like me) you have lost of choices but can’t do everything. For example:
Flying to San Francisco, going to Yosemite, then maybe Kings and Sequoia; maybe Death Valley; maybe Joshua Tree (2 of 3 are do-able). If you do either of the latter, you could fly out of Las Vegas. There are a few amazing red rock areas near Las Vegas so it’s not all bright lights. The problem with going to Las Vegas is you’re perilously close to Arizona and the Grand Canyon so you might want to go there… Or you could just go north from San Francisco before Yosemite and see the spectacular coast and redwoods.
Flying into San Diego (or LAX, but see above), going to Joshua Tree and then picking up one or two of the national parks above, then seeing the coast between LA and SF, before flying out of San Francisco. Flying into (and out of) Palm Springs is an option too.
The choice of itinerary definitely depends on the time of year. The Sierra Nevada passes are closed mostly November-June for snow, but if you’re going in the summer heading North and mountains is a good choice as you will bake in the desert. If you do go to the desert in the summer, you can at least be up and out before 6am (jet lag) and do your hiking before it gets too hot.
Consider an America the Beautiful pass. For $80 a car-full can enter and park in all the national parks, monuments and national forests. And then you have to book a return trip within the next year because it would be wasteful not to…