Another suggestion: get the bike and start in San Diego, head up the range just east of I15 towards Hemet, from there go up over the mountains through Big Bear to Lucerne Valley if there hasn't been any recent snow, but if there is stay lower and go through 29 Palms to Lucerne valley. From there head west through Lake Elizabeth if no snow or Sierra Hwy if there is, then towards Ojai and up along the coast as far as you have time. Some great roads and nice scenery while avoiding most of that mess called LA. If you're flying in, you can probably fly into San Diego for the same price or less, or fly into La and back from San Diego and take the train from La to San Diego for something different.
"Le bonheur est un voyage, pas une destination"