With so little time, you'll have to fly to do what you want to accomplish. Luckily the fares are not that expensive with competition on the routes.
You should travel from LA to Vegas, tour the nearby Grand Canyon, then fly to San Francisco. You'll only get a taste of the places you want to visit, unless you have more time.
Depending on your interests, suggest three or four days in LA, three days in Vegas and the Grand Canyon; and the rest of the time in the Bay Area.
You probably should start a new thread on this forum, as the initial topic was about travel to South America.