RE: Driving from SFO - LAX, this is a huge time commitment. Hwy 5 takes 6 hours, Hwy 101 takes 8 hours, and Hwy 1 takes 10-12 hours depending on the weather. These times are conservative during Winter Weather. Do not be deceived by the mileage on Hwy. 1, since the entire length of Big Sur (to San Simeon/Hearst Castle) is driven at approximately 15-40 miles per hour, not 60! It is very narrow, winding, and scary (but stunning).
A better bet would be to rent a car and drive down the coast PART WAY for a day. I would start out early (and stop for breakfast in Santa Cruz or Capitola if you must), then head directly for the Monterey Bay Aquarium which is not-to-be-missed. Cannery Row and neighboring Pacific Grove are great lunch options. Spend the afternoon in Carmel or venturing into Big Sur before heading back to the Bay Area. Trying to cross the mountains through Carmel Valley to Hwy. 101 (via State Rte. 16) is discouraged in winter. HAVE FUN!