The Bay Area is definitely not within Central California, taken as a sociogeographic term. The Central California Coast is the coastal region between roughly Santa Barbara and Point Lobos, centered on SLO. There is also another inland definition of Central California: https://en.wikipedia.org/wiki/Central_California
The same is true for Northern and Southern California. There's no official distinction. Calling the Bay Area part of Northern California places too much emphasis on the Los Angeles area. By analogy, saying that "North" begins at the Transverse Ranges is like saying that "Upstate" begins at Yonkers. Ridiculous.
http://en.wikipedia.org/wiki/Northern_California
"Northern California is the northern portion of the U.S. state of California. The San Francisco Bay Area (which includes the cities of San Francisco, Oakland, and San Jose), and Sacramento (the state capital) as well as its metropolitan area are the main population centers."
I have found that (Bay Area subset of N. CA) is a very common misconception of people who have recently moved to the area.