The San Francisco Bay is rather large. There is only the western entrance and north "throat" of the bay situated at San Francisco. It looks like this from the middle of the Bay Bridge (with Alcatraz in the center):

The whole bay is enormous, it goes down to San Jose which is not a big distance on the map and what we were driving around, can be hardly seen on the California map - but it would take one and a half day to drive through the state from North to the South. Here is one more pictue of the bay from a little further: