My favorite blackberrying spot is up in Humboldt county, but that's a bit far to drive. You can also find huckleberries and salmonberries around, and they're quite nice, too.

take a day trip to the russian river area, it's crawling with blackberries :)

pulled this from my weekend sherpa newletter that just came this morning:

THE HIKE: Beach, blanket, food. If this is your ideal trio, then a daytrip to Point Reyes and the nearby town of Point Reyes Station makes a nice picnic combo. A 1.5-mile flat hike to Abbotts Lagoon is just enough to work up an appetite. Mid-way through, blackberry bushes line the trail, and right now they're ripe! On windy days, lay a blanket on the leeward side of the large sand dunes at the lagoon. When the wind isn't kickin', keep going past the lagoon for another .5 mile to the beach. (Watch for nesting snow plovers; they enjoy this spot too.) After feasting on picnic fare, walk along the beach in search of sand dollars. They're not hard to find and make great window-ledge décor.

Santa Cruz Mountains and Watsonville Mountains like Mt Madonna have tons of wild blackberry shrubs.
I use to live in Santa Cruz...I miss that place so much.

Spencer

The Presidio used to be a good place for berrypicking. In fact, I used to have maps of all the good berryspots there--it's changed though in a decade so I'd recommend scoping it out as a hike and then going back to gather.

The Sacramento Delta! there are blackberry bushes on the delta and on most of the sloughs. Pilot a boat alongside and you can fill buckets-full of berries.

In the South Bay, they are right ajacent to the parking lot @ Pachetti Open Space/Winery.
It is in the Stevens Creek area, right above the Sunnyvale Rod & Gun club range.
Take Stevens Canyon Road( from Foothill Expressway) up aroround the Reservior, jog to the Right up Montebello Road( it is a dead end at the top, but damn what a view!) take a few curves and the entrance will be on the Left.
Beware of cyclists though, they fly downthis hill FAST!
The parking lot is surrounded by plants, which may have some berries still.
Take time to explore this park, with it's great views and moderate trails, old orchards still stand and I think this is the time to get pears!
Enjoy the wildlife here as well, you may see the resident Bobcat if you are lucky.
Enjoy :-)