Not dis-similar to the first time we visited the States in 1989.
Flew to LA, drove up the coast to SF (overnights in Santa Barbara and Monterey) then on to Yosemite and Grand Canyon.
A few more detailed thoughts...
Definitely agree that unless big cities are your thing, plan to spend as little time as possible in LA. Even the coach shuttle from LAX to Alamo and the drive over to the freeway made us nervous.
SF is a bit better, but we stayed in Walnut Creek (just south of Oakland) which allows you to catch the BART train into the city centre. Then used the Muni Metro to get round and visit locs like Golden Gate Park.
Yosemite is awesome but you do need to book ahead if you want to stay in the park. Snow on Tioga already mentioned, also worth noting that east of the pass if you're driving via Tonopah to the Grand Canyon, there's very little in the way of services or amenities until you get to Tonopah. So don't play chicken with the gas tank and carry some food and pleny of water - the lush terrain of Yosemite rapidly turns into arid desert.
Grand Canyon will be the highlight. If you can, book two nights so you can take a short hike down into the canyon. Both times we went there, walked down to Plateau Point which is around a 12 mile round trip (but takes around 9 hours as the climb out is surprisingly steep). Or for a shorter walk turn back at Indian Gardens. You will earn your steak dinner in the restaurant that night.
If time permits you might want to head out towards Monument Valley.
Other California locs worth doing are Death Valley (again, plenty of gas, food and water), Sequoia National Park and the road down to Mineral King are well worth doing.
On a general note, don't be put off by driving longer distances than you would in the UK. Once outside the cities, barring accidents the freeways and interstates are generally free flowing. Single carriageway roads tend to have passing lanes and shoulders, quite unlike our A Roads here. Even sticking to the speed limits you could easily cover 400 - 500 miles on a "run" day. Our very first trip we made the mistake of having several 150 - 200 mile days and were arriving in our destination just after lunchtime, we could have travelled much further and seen much more.
The biggest downside to driving in the US (apart from getting used to undertaking on four lane freeways!) is fatigue. Many American roads have long dead straight sections especially in the desert, where you can be going for fifteen miles though dead straight terain with heat shimmering, a slight curve through a low range of hills then another 15 mile dead straight. Even the most alert driver might find it hard not to nod off (hint: don't use cruise control). There's also the tendency for speed to creep up to 80 MPH at which point you can guarantee there will be a smokie waiting behind a tumbleweed, to get you!
Whatever you decide enjoy your holiday. It's ten years now since we've been to the States/Canada and really must think about going back.