LAX - San Diego (visit Tijuana by train - hire cars not covered to cross border)
SD - Palm Springs (be ther on Thurs nite)
PS - Scottsdale (stay Holiday Inn Express, visit Fashion Mall)
S - Sedona - Flagstaff (stay HIE at edge of town, visit Meteor Crater, Grand Canyon)
F - Las Vegas via Lake Havasu, Hoover Dam
LV ------ Yosemite (u outa time! leave for another trip
LV - LAX via Bartsow
Do LAX - San Fran, Yosmite another trip
Check mileages and times, don't rush thro' it
We did a trip with same locations in 2 weeks and didn't feel rushed.
3 days LAX, drive to LV 3 nights, drive to Grand Canyon and stay 1/2 nights there, drive to Sedona stay there- make sure you do the driving there during day, fabulous views. Palm springs , not quite sure why you would want to stay there longer than one night, we stayed 3 but only because we met some friends, drive to San Diego stay 3 days, you can drive to border at Tijuana and park car ,then do a short bus ride- but really it will definitely not be a highlight of your vacation, I stayed 3 hours and was very happy to leave again.
Interesting trip would be round trip from SF:
SF arrive and stay day 1-2
Drive to LAX with 1 or 2 stops along the way ( day 3-4)
Stay in LAX 2 days (day 5-6)
Drive to and stay 2 nights in San Diego (day 7-8)
Drive to Sedona with one stop on the way (day 9-10)
Drive to Grand Canyon and stay one night (day 11-12)
Drive to and stay 2/3 nights in Las Vegas (day 13/15)
Drive to and stay 3 nights in Yosemite (16/18)
Drive to San Francisco , stay on more night before you fly back
This would probably have been my itinerary if I would have had 3 weeks instead of 2. You need to love driving, because that is what you'll be doing a lot of, get a nice car, convertible. Don't think you'll manage if you'd stick rigorously to only 5 hrs a day in the car.. some stretches will require 7/8 hrs.
And yes, you may not have time to see all that the various places have to offer, but you will see a lot and can always come back to where you'd want to spend more time. Touring in US will always be a case of compromising.
If you want to break up longer journeys and need more days, maybe forget about driving to Grand Canyon/Sedona and do a day (or overnight) trip from Las Vegas to Grand canyon instead- by helicopter/plane.