I live in the Bay Area, but rarely backpack here, because I've been kind of disappointed at the offerings. I have a personal Top Fifteen list of most beautiful hikes in the Bay Area; I think only one of those trails has any backcountry campgrounds. Thus, I Dayhike.
Sunol, including Little Yosemite, is okay but is nothing to write home about. It's a lot prettier in April-early May, when it's lush and the wildflowers are out.
Point Reyes can be gorgeous; as long as you don't mind potential fog, the lack of solitude, and being hounded at your campsite by sixteen hungry raccoons.
The very best I've found is that backcountry campground in Big Basin, near the three waterfalls. I think it's called "Sunset." The campground is not itself extraordinary; but the hike there and back is. Do it as a loop. ~12-13 miles total.
I'd be curious if others here have uncovered any Bay Area backcountry trips that are really nice.
I suspect most of them would be found on the Peninsula. For instance, Butano State Park is nice, and there is a site about 5 miles in that I've never checked out.