Needish

Sydney

A few suggestions:
-the Fillmore jazz festival is in SF on July 5th and 6th. I've never been but plan to go this year ("the largest free jazz festival on the west coast"). And while you're on Fillmore street, there are lots of cute shops to wander in and out of as well
-one fun day trip north of SF is to Point Reyes National Park. It only takes about 1 hour by car to get there. You can go hiking, shuck your own oysters, see the lighthouse, enjoy the beach, etc. You can also go to Cowgirl Creamery in Point Reyes Station for delicious cheese! And, I think you can rent kayaks, etc. for the day. You can also camp overnight.
-I assume you are driving down the coast since you fly out of LA? Driving along highway 1 is a very scenic route. Definitely stop at one of the many missions (in Carmel, in Santa Barbara, etc.). San Luis Obispo, Monterey, and Carmel are cute and have some good shopping. Monterey also has the aquarium which is great regardless of your age!
-For shopping in SF, you definitely need to take a trip to Union Square!
-Also in SF: walking across the Golden Gate bridge is a typical thing to do, as is going to the top of Coit Tower for a great view of the city. After Coit Tower you can walk to (or take the bus to) the Buena Vista Cafe for some great irish coffee. It's a tad expensive but worth the show they put on. Ghiradelli Square is also in that area which has AMAZING ice cream sundaes, etc.

kfurlong

Sydney has definitely done a good job giving you SF recommendations! As for LA and further south of the Bay Area, I would recommend:
- If you ARE driving down the coast, Santa Barbara is another really cute place to stop. It's a typical 'beach town' in California, with a university and lots of beach space. Also, I hear San Luis Obispo is adorable, but it sounds like that's been mentioned already.
- LA has a LOT to do, but if you like shopping and/or celebrity culture, head down to Rodeo Drive in Beverly Hills. You likely won't be able to afford much, but it's fun to window shop in the really ritzy stores (Tiffany's, Gucci, etc) and pretend! Also if you're down there, ask for Sprinkles - it's a cupcake shop that makes the most amazing afternoon snacks!!
- Venice Beach is kind of on the other end of the spectrum, a kind of alternative beach community more towards the water (duh), where you can walk along the beach walk and find anything from cheap knock off sunglasses to original art and body piercing. Tons of good people watching, and you'll pass by the famous "Muscle Beach" where you can see bodybuilders training. Good fun!
Anyway, those are my thoughts about LA and more southern-ly places in California, so hopefully they're helpful!! Have fun!