Yeah, I really like the rural National Forest Campgrounds. It's been a while since I went camping with the family, we have too many pets to leave home these days (over a dozen chickens, 3 cats, and the dog -- plus we just brought in a feral pregnant cat who had 5 kittens that are now a few weeks old).
Stanislaus River Campground is one of my favorite places is the state to camp at, and it's pretty rural. $12/night, first come first served.
Link:
Stanislaus National Forest - Stanislaus River Campground
www.fs.usda.gov