Richard at Cyclelicious put up a post about bike camping sites in California state parks and I thought I'd add a few of my own favorite sites for biking and camping. All of these sites except perhaps Pleasant boat-in campground at Loon Lake are doable with kids.
Wildcat Camp and Coast Camp, Point Reyes National Seashore. Coast camp is about a 2 mile ride from the trailhead near the youth hostel, off the Limantour beach road. Wildcat camp is about a 6 1/2 mile ride from Bear Valley visitor center. More info and permits available at Bear Valley visitor center for either campground. You can ride from Embarcadero BART in San Francisco to make a weekend overnight.
Samuel P Taylor State Park, Fairfax, Marin County. Peppermill Creek flows through the middle of the park, and the campsites are situated among towering redwood trees. There's an off-road dirt hike/bike trail connecting from Fairfax, I ride it on a road bike with skinny tires no problem. The hike/bike path runs right through the park and continues another 3 paved miles to the intersection of Sir Francis Drake Boulevard and Platform Bridge Road. Campsites are usually booked ahead, but after 6pm the day use area is used as an overflow campground until 9am. We used to do this a lot, but it's been a few years so call ahead to confirm the day use is still available for camping after 6pm.
Loon Lake campground or Pleasant boat-in campground at Loon Lake, northeast of Placerville. Loon Lake is at about 6,000 feet on the edge of the Desolation Wilderness. The main campground is drive-in, or you can bike to the boat-in campsites. You can circle the lake on a mountain bike, combining the southside hiking trail with some class V and VI off-road trails on the east and north sides of the lake (connect near Spider Lake). I could not believe they get 4x4's up and down these trails, I was having a heck of a time on a mountain bike. Suspension would have helped. This is a boat-in campsite which is also bike/hike accessible.
Sly Park/Jenkinson Lake is at about 3,500 feet in the Eldorado Hills near Pollock Pines off Highway 50. Campgrounds are drive-in, the attraction is an outstanding 7 mile loop that circles the lake. It's about 70% narrow single-track that flows extremely well, and about 20% wide dirt trail. Nothing too technical except for a few rocky sections where the signs say to walk your bike. The lands are part of El Dorado Irrigation District.
Mackerricher State Park, near Fort Bragg in Mendocino County. Drive-in campground with one loop reserved for tents (no RVs). An old (paved) log haul road is open to bikes and hikers and runs about 8 miles from the park to downtown Fort Bragg. You can also go north on the paved trail for about 6 miles to the dunes at 10 mile beach. The little lake in the park is stocked with trout. We once counted 15 osprey hovering over us, and saw one swoop down and grab a fish out of the water between us and our bobbers! Coin-operated showers.
Sugar Pine Point, Lake Tahoe. The park includes a beach on the lake as well as many trails leading off into the Desolation Wilderness. Coin-operated showers are a nice amenity.