It depends on what you want to see...
You mentioned the beach (and driving on the beach). In that case, I would hit up the Dunes in Pismo. For like $3, you get to drive along the water until you reach the dunes. It's pretty cool.
If you like scenery... check out Yosemite National Park and the Black Mountains along Route 66. Cali is filled with mountains, so there are plenty of places to checkout.
If you're into checking out Gold Rush Americana type things (as I am), there are TONS of ghost towns right off some of the major freeways. Grab a book or two on the subject or checkout the website
ghosttowngallery.com. It's VERY basic, but if you find one that looks interesting based on the photos, just do a search for that particular ghost town for more info.
If you're into natural wonders or stuff you just don't see everyday... why not head over to something like
The Sliding Rocks of Racetrack Playa and Ubehebe Crater? Or how about checking out a
The Albatross, a downed CIA plane from the 50's just sitting on the side of a mountain?
The sites to see are countless! I've lived in SoCal my whole life and have been exploring it for several years. Just find what's important for you to see and make a plan on Google Maps.
Good luck and have fun! Be sure to take LOTS of photos and make sure you're in them. No one wants to see the same photos that you can find on the web. They're truly that much more special when you're involved in the adventure.