I'll start this as a community wiki and seed it with a few places. While places like Shasta and the Sierra may be within 3 hours drive, this is usually not the case once traffic and speed limits are factored in. Note that nearly all of these sites will require reservations, and may fill up quickly in busy months.
- Dispersed Camping: "wild camping"; find your own campsite, water, etc.
- Primitive Campsites: Designated spots that usually include a water source, pit toilet, and sometimes tables. Unless you reserve a group site you are likely to have other people nearby.
Samual P Taylor State Park
Point Reyes National Seashore
Primitive campsites only; may be crowded in good weather but you can also have it to yourself in the shoulder season. Extensive trails for long hikes, excellent mix of terrain and local wildlife.
Golden Gate National Recreation Area
Four campgrounds scattered around the Marin headlands.
In the Bay
Angel Island State Park
A number of primitive campsites and group sites. Take the ferry to get there if you don't have a boat of your own.
Castle Rock State Park
Good for rock climbing. The only overnight options are "primitive campsites".
Henry W. Coe State Park
As the largest State Park in Northern California, Henry Coe is also one of the few places around the SF Bay Area to offer true "dispersed camping".
Big Basin Redwoods State Park
The oldest State Park in California offers an extensive network of trails, a few primitive campsites for those doing the Skyline to the Sea trail, and some car camping sites scattered around the park headquarters.