First of all, superstar, I hope you have a great trip.
As vandal and buckgully have noted, there are basically three practical ways to get from LA to San Francisco. (Note that the San Francisco locals generally don’t use the term “San Fran” even though everyone else in all of Christendom uses the term.)
- Drive the direct route (5 to 6 hours)
- Drive the scenic route (12-14 hours)
If you drive the direct route, the emphasis is on “direct.” I-5 straight up. Not very scenic. Sometimes crappy traffic but usually not too bad.
If you drive the scenic route, the emphasis is on “scenic.” Much of this drive looks like something out of a tv commercial. Amazing cliffs, and view of the sun out over the Pacific most of the way.
Flying is relatively cheap. Southwest Airlines is usually the cheapest. Note that on Southwest you don’t have an assigned seat, so get there an hour early so you can check in.
Note that the BART (the SF Subway) goes to the Oakland Airport, but not to the San Francisco Airport. You may want to rent (or, in Ozzy “hire”) a car when you are in San Francisco. It is a pain to drive around the city, and an even bigger pain to park, but you can get to some cool stuff that you wouldn’t be able to see otherwise.
Much to our everlasting shame, and to my everlasting frustration, the train is, as buckgully noted, probably not a practical option. Not only is it slow, but last time I checked you had to take a, ahem, “motor coach” (aka a bus) from LA to Bakersfield, and then get take the train from Bakersfield.
When you are in San Francisco, be sure to go over the Golden Gate Bridge, and go up to Mt. Tam (aka Mount Tamalpais). There is an AMAZING view from the fire look out post up there. You can see the entire San Francisco Bay, and Marin County, and the Pacific Ocean. Also visit the Exploratorium, which is one of the coolest science museums in the world.
As to the Grand Canyon, you absolutely must do whatever you can to see it. Coming all the way to Vegas and not going to the Canyon is like going all the way to, I don’t know, Brisbane, and then deciding it’s too much trouble to see the Great Barrier Reef. From Vegas, probably the best way to get to the Canyon is to drive to the North Rim. The North Rim is less crowded, less touristy. And mind blowing. To me the Grand Canyon is like Shakespeare’s Plays, or the Great Barrier Reef. You’ve heard so many people say so many good things about it, that you have to think it’s overrated. But it’s not.