San Francisco Camping areas

[MoGas]

I'm looking to do a family trip to San Francisco in mid October and I was hoping to find some campgrounds in the area. I've looked into the Golden Gate Park, and that seems cool. I would like to be able to be close to the city for our visit purpose. Preferably somewhere that I would be able to access public transportation easily. Public or private campgrounds, doesn't matter to us. We will be in a tent, have our own "facilities" if necessary, and are mostly looking for a place to crash in the evenings. Even a back yard would work.

Any ideas?

Thanks,
Dave