Well, from LA, if you continue down the 5 into San Diego, you can catch the 8, which goes over into Arizona and then I think you have to decide whether to stay with the 8 or switch to the 10 (it's been a while since I've driven that way into Arizona).
San Diego has the beaches, (Coronado and the famous hotel being two of the best places to see), the Zoo has a new baby panda (just born 2-3 days ago), there's always Sea World, we have the Wild Animal Park (animals in their "natural" habitats)...close proximity to Mexico. Basically San Diego and the surrounding county gives you all four types of habitat: coast, inland valleys, mountains, and deserts, so anything you could think of to do you could probably find here in the area! Of course, there's Disneyland in Anaheim, Magic Mountain, Knotts' Berry Farm, and a number of other theme parks to go to as well, but I don't know too much about them. Probably if you did a Yahoo search about places to see for the Southern California area, you'd come across a LOT of ideas. I hope this helps!