These are two separate road trips I took while living in California because time was always an issue. But, if you have a spare week or two, a drive up the California coast is truly idyllic.
Los Feliz, California, United States
Fly into Burbank (it's MUCH easier to navigate than LAX) and then stay on the east side of town. I love Los Feliz because it captures the West Coast vibe, while still maintaining the walkable community feel you get in an East Coast town. Stay here a day or two to explore nearby Griffith Park, grab a slice at House of Pies, and catch either Jeff Goldblum at Rockwell or Marty and Elayne (remember Swingers?) at the Dresden.
Carpinteria, California, United States
Next, take a drive up the 101 toward Santa Barbara. About halfway through the drive, you'll get a hankering for coffee. The Lucky Llama is your place. It's a cute little shop right off the main street, and has an amazing chai latte (if that's your thing). The outdoor patio is a nice space to take in fresh air and savor your coffee.
You'll probably want to spend a couple of days in Santa Barbara. Knock out Main Street on day one, walking from north to south -- check out the Santa Barbara Art Gallery, grab tacos at Lilly's, and take a stroll along the beach. On day two, venture out to the local wineries, as well as the Santa Barbara Botanic Garden.
If you love wine and cute little Dutch towns, Solvang is your place. There are lots of wineries in nearby Los Olivos, but the main attractions are the Dutch shops (think: small buildings with windmills) along the main street. It's magical.
Once you've driven further up the Central Coast, take time to reflect in Morro Bay, a quiet coastal town. It's defining feature is Morro Rock at the entrance of Morro Bay Harbor. You shouldn't climb the rock, but there are paths and sitting areas along the base. Up the road, you'll find small shops and restaurants, including a surprisingly decent pizza shop.
Big Sur, California, United States
Ah, now for the big show. A drive through Big Sur is life-changing. Windy roads, cool breezes, and undeniably spectacular views. Stop at key viewpoints along the road (I always prefer the less crowded stops) where you can look out across the Pacific -- and sometimes even find yourself above the clouds. Take your time, take it all in.
Another small town along the coast, with a stunning coastal view. You'll find lots of shopping and restaurants here, including some awesome live music venues (Half Moon Bay Brewing Company, Pasta Moon, and Seville Tapas all have great music and food).
Finally, a drive from SoCal to NorCal isn't complete without a stop in San Francisco. There are touristy things worth doing: ride a bike across the Golden Gate, ride a trolley, check out the seals on the Embarcadero, tour Alcatraz. But, you should also spend some time across the Bay. Oakland is building up quickly, and Berkeley is the cute, hippy town you expect of California. Make sure to hit Cheese Board, a bakery, cheese, and pizza shop in Berkeley that sells only one style of veggie pizza each day (trust me, it's amazing, and I'm a meat and potatoes girl). Try to get there at off-peak; the line can get really long.
If you want a good sense of the California lifestyle in a short amount of time, this is a great taste of the state. If you choose to extend your trip to Napa, Sonoma, Lake Tahoe, Yosemite, or the many Sequoia forests farther north, I highly recommend those places as well.