While in LA, (besides the usual Hollywood & beach visit) I would recommend the griffith observatory for views and a hike, the museums on Wilshire like LACMA and Peterson Automotive, and Farmer’s Market/the Grove for shopping.
On your drive up, definitely take Pacific Coast Highway, and stop wherever you see something interesting… Carpinteria, Santa Barbara, Hearst Castle, Monterrey. There’s a great website called roadtripusa.com that has a good list that I usually check before for ideas.
And may I make one more suggestion, If you’re gonna be all the way in SF, you may as well make a trip to Yosemite!! It’s gorgeous!! My friends have done it as a daytrip once, but you would probably want to spend at least one night there. Just a thought! Have fun, and feel free to ask more questions!!
p.s… do try In-n-Out while visiting!