From SF I would head across to Tahoe and stay on the west shore. Nice state park there and great beach for the kids. No hook ups but beautiful.
Ed Z'berg Sugar Pine Point State ParkThen you can head over to hwy 395 and take your time going down thru the sights that are on the east Sierras. I know there are several State parks - the link above will give you info all all the CA parks. Red Rock SP above Mojave is beautiful.
Once you drop off in LV, you can head over to LA or Santa Barbara and work your way north on the coast. There is a great state park at
Leo Carrillo SP. it has a great beach and you can then head up Hwy 1 all the way back to SF. Below Big Sur we like to camp at
Plaskett Creek Campground in Los Padres NF.
The most important thing while camping on the coast during the summer is to make your reservations or there will be nowhere to stay. Sorry to say! 6 months out for reservations, private are more available it seems.
Have fun, planning is half of it!