Haven't found anything of interest in Berzerkley unless you are from Banglore, Calcutta, or Delhi.
Take PCH down from Geary in SFO, stopping at Mavericks, Half Moon Bay, Santa Cruz, and then on to Monterrey and Carmel.
Drive north out of SFO across Golden Gate to Russian River Road and follow it to the Pacific and then South on PCH through Bodega Bay (veer over to Bodega) and then on South to the Golden Gate.
Napa and Sonoma if you like wine, but try to do them on a weekday if possible, it's a lot less crowded. If you are interested in wine, make a reservation in advance to tour Jordan up in Sonoma County. It is an incredible tour.
Do the tourist crap - Pier 39 and then 36, 42, 48 mile (whatver the number) drive. Do this drive backwards, starting at Twin Oeaks and then going West to east thru Lincoln Park to the Presidio - great views of the bridge.
I'm not a fan of Muir Woods, but lots of people enjoy it and it's probably a 30 minute drive from Oakland.
SFO has several neighborhoods which are good for half a day or less - Pacific Heights, Marina District, north Beach, Chinatown, Market, SOM, Fisherman's Wharf, Saulsalito, Tiburon. Killing a weekend afternoon with a few beers next to the water at one of the bars in Tiburon is really enjoyable. Usually plenty of scenery around there, excluding a sometmes sober Grace Slick, who lives half way up the hill.
In Oakland there is Jack London Square, and Rockridge, then pretty much nothing else. San Fran is not that far away, just across the Bay Bridge by car, or you can take the BART tube over. For things near the area, Napa/Sonoma wineries, Monterrey, Big Sur, Carmel are all easy day trips.
I think we will be working just a block or so from Jack London Square. I know all about the north of the golden gate thing. Love it up there but won't have too much time for that kind of drive.
There is a relatively new music venue in SFO - someting like Great American Music Hall or something like that. Much like the Fillmore, but probably nicer - what isn't - at least it won't be on the second floor above a check cashing store.
If you're a baseball fan, take the ferry from Jack London Square directly to the AT&T Park to see the Giants - and a really picturesque baseball venue. The ferry stops right behind the park (McCovey Cove) and the ride is neat.
Go to a Oakland Raider home game wearing black. Do not by any circumstance wear any other team apparel. If you don't have black go in white or a neutral color for that week. Great game day atmosphere.