Disclaimer: I live here.
Driving between LA and SF is doable over a week. Certainly lots to see along the way.
There's also value in staying in a specific region and really getting to know it. IMO, your August timeframe probably eliminates any national parks. Shame, because Sequoia is one of my favorite places on this planet.
Some don't realize how massive the LA region is.
MAPfrappe shows that drawing a shape around Santa Barbara, LA, Orange County, and Palm Springs is essentially the distance between Iowa City and Chicago.
You could do a little bit of everything without even leaving SoCal. One month is not even enough time to see all of LA:
- Kayak through the South Pacific (Channel Islands National Park)
- Blast off into space (Space Shuttle @ California Sci Center)
- One of the world's greatest theme parks (Disneyland)
- Climb Griffith Park (Hollywood sign and observatory)
- Discover King Tut's tomb (Last world tour @ California Sci Center)
- Hike California's famed coast (Palos Verdes or Laguna Beach)
- Paddleboard around sea lions (Newport Beach)
- Experience the echoes of conquistadors (Old Mission Santa Barbara, etc.)
- Beach and surfing (Malibu, Santa Monica, Huntington Beach, etc.)
- Tour of mansions in movies (Hollyhock, Gamble House, etc.)
There is so much. Impossible to distill down without knowing more about you.