You can rely on public transportation within the Bay Area. The BART (metro) and CalTrain (train) are good for commuting or covering large distances. Each municipality has their own bus system, so you can get around within a city that way or better yet, via walking or bicycling. Note that you can take your bicycle on all means of mass transit, though bikes are forbidden from BART during certain rush hours. This will be easier than dealing with traffic or parking. Taxis are an expensive last resort.
The downside is that for getting out of the Bay Area, public transportation is more difficult. You can take a Greyhound bus or shuttle or Amtrak (train) to some places, but then you will definitely have to walk or bicycle, and the towns tend to be more spread-out. (I don't know about taking bike on Greyhound.) Also, even within the Bay Area, public transit can be relatively expensive and can be slow, depending.
One option is to purchase a motorcycle. The Bay Area motorcycle scene has a strong presence, there are many nice places to ride, parking is easier, and lanesplitting in California is legal (meaning traffic affects you less). Also, the good climate means you can ride year-round. This is my preferred solution.