I drove from LA to San Fran but not in one go. If you went on the main highways you can get there in the time mentioned my mushroom25.
However, it is a much better idea to drive up the Pacific Coast Highway and see Santa Barbara, Big Sur, Carmel and Monterey en-route.
The drive is amazing!!!!!!!! We stayed overnight in Monterey.
As for San Fran to Vegas. Could you not get a hire car from Hertz ? they do one way / different state drop offs, so you wouldn't have to drive back to vegas...It's a long way!!!
I've done this trip a couple of times and always fly from San Fran (Oakland airport) to Vegas. Never paid more than �50 and the flight is only about 1.5 hours.