The things not to miss are: SF, “Highway 1” SF-LA, Las Vegas, Zion & Bryce Canyon, Grand Canyon, San Diego.
Yosemite is also spectacular BUT will add 2 full days driving to/from anywhere else, so skip it so you can really enjoy the other places. Also are you going in Winter? Because you cannot cross the eastern border of the park in Winter, too much snow. So then no point *at all* to try to drive from SF to Vegas that way.
I would plan:
4 days SF (America’s best city – enjoy it! – don’t get a car for the city; Get your car on your 3rd or 4th day and do a day trip to Napa Valley wine country and/or see the Redwood Forest)
Drive to Monterey on the fast road (1 hr) – see aquarium, art village Carmel, drive “9 Mile Drive” and spend the night in Monterey
1 day Coast highway #1 Monterey-San Luis Obispo stopping at Hearst Castle (make a tour reservation). Lunch in Lucia.
San Luis Obispo-LA (3 hrs)
4 days LA & San Diego
Fly San Diego to Las Vegas (it’s a 7 hour, boring drive)
2 days Las Vegas – stay somewhere between Venetian and Aria hotels
1 week: from Las Vegas drive a loop: Vegas – Zion – Bryce – Grand Canyon – Vegas. Then fly out from Vegas.
As for LA some people like it, I do, but it’s not a walking city – some small walking areas and a car in between them. It’s so big I think of it as three cities: West, Middle and Downtown. In the west: Santa Monica, Venice (Abbott Kinney Blvd.). In the middle part, West Hollywood (gay-borhood) La Brea/Wilshire area, Hollywood/Vine, Silverlake (alternative gay-borhood) and Los Feliz. Downtown is very disappointing to most Europeans, it was completely run down and is actually a very busy Mexican/Central American downtown. A few “hip” places opened, but really not that many. I like visiting the great old buildings there – very faded glory.
San Diego has a big downtown which is mostly new but very enjoyable – shopping, restaurants, cafes, and a waterfront. San Diego has beautiful beaches and is just a great place to hang out and relax. There is also a great gay-borhood at Hillcrest (near University/Washington Boulevards around 6th Avenue.) Lots of “real people” and very easygoing compared to LA (which is full of “beautiful people”)