The Bay Area is the area in California, containing San Francisco, Oakland, San Jose and other urban centres. It's fairly extended, with millions of inhabitants. There's a plethora of highways, and it's probably better to see the Area as one huge city, with "The City" (San Francisco) as its cultural centre.
Going North or EastEdit
You can take the BART to Richmond (about 4 US$), get off, walk East, where there is the on ramp to the I-80 East. See Google maps.
Go to the 19th Avenue, which is also I-1. Find a good traffic light while walking South. You can even start in the Golden Gate Park.
Take the I-5 if you want to get there fast. Otherwise you might better off with the I-1 and/or I-101.