Your plans are very ambitious. In the 9 days you describe, you mentioned Grand Canyon, Joshua Tree, Yosemite, Las Vegas, and San Francisco. Unless you are spending less then a day at each one of those locations, you are looking at a few weeks worth of travel by car. Keep in mind that it isn't just the physical distance between the locations, but also the amount of time it actually takes to drive.
For example, I often do this 24 mile drive for work. Depending on when I leave, the road conditions and what not, the drive can be anything from 25 minutes to an 1.5 hours. Here's my advice....
Trip 1) Take Highway 1 up the coast north of LA all the way up to Monterrey Bay. Beautiful drive...you can see Hurst Castle if you want. There's a beautiful aquarium in Monterrey. You can continue north up to San Francisco. Stay there and see the sights. You'll be on Day 2 by then. Then you can swing southeast-ish down to Yosemite. You could then take the desert highway out to Las Vegas (skip Joshua Tree...there's nothing but sand and rocks and the trees. You will see the exact same sand, rocks, and trees on the drive to Las Vegas). It is a very long drive from San Francisco through Yosemite to Las Vegas. If you can make it, you'll be completely dominated. You hang in Las Vegas, and then drive back to LA. You'll get back and have time to go to Santa Monica or see whatever around LA.
Trip 2) Drive east of LA up to Las Vegas. Hang for a day. Drive east up to Zion (I high recommend this....Zion is gorgeous). Drive south to Grand Canyon. Beautiful. Skip Lake Havasu because you aren't a 22yr old trying to loose their virginity while puking melon balls out your nose. Continue around, skipping Joshua Tree again (see reasons above). Drive down to San Diego (a beautiful city...unlike LA). You can go to the best Zoo in the world, Balboa park, go out to Coronado if you want. If you feel like a horrible adventure, go to TJ (you might die...like actually die. Drug wars aren't fun). You then drive north through North San Diego county, Orange County, and then up to LA County.
Ok...so here's the thing. This totally depends on the exact timing of your trip. This also depends on what season it is like here. If there's been a storm, the passes through the mountains will be closed (at worse) or require snow chains/ropes (at best) and you can triple your drive time. It also totally depends on what you want to see. Nature and beauty...or city life complete with crack whores and drug wars...or something in between.
I need to go on a trip now. I seriously wouldn't mind going up to Zion.
~Jeordam
Saving the Princess, Humanity, or the World-Entire since 1985