It takes at least a month to do justice to the core of California, two months if you want to see the whole state.
This will start your trip off on a fine note but if you have to fly out of San Francisco also, you might be very reluctant to leave. If you do arrive in San Francisco, stay a few days then head east to Yosemite National Park (4 hour drive), south along the coast toward Los Angeles, or north to see the Redwoods.
There are things you should see in LA (e.g., the Getty Museum) and it is probably is better to see them first so that you can relax and enjoy the rest of the state later. If you fly back out of LA, you probably won't be sorry to get on the plane.
If you want to concentrate on the Sierra Mountains, Yosemite National Park and Lake Tahoe, you can avoid the engulfing cities of California altogether by flying into Reno, which is only about an hour from Tahoe.
California is
all about driving and Californians appreciate fine cars. Half of the Rolls Royces
and Ferraris sold in the US are sold in California. Although city freeways are
crowded, there are many mountain roads where a well-balanced car is a joy to
drive. My best California tours were in
an Acura
NSX and a Dodge minivan, because I could
take my mountain bike and all my cameras.