Some of the places we've taken the kids are:
Kings Canyon/Sequoia Natl Park
Calaveras Big Trees
Moaning Caverns
Twin Lakes (on the 395) the fishing was great
Bodie (also on the 395)
I've never been there but heard Lake Mary is really cool
Pismo. Once we found out there was a rocket launch at Vandenberg so we went to see that while we were there. You can drive on the beach and rent ATV's. We enjoyed the hike out to Oso Flaco Lake, lots of birds and an isolated beach.
Hearst Castle
Refugio
Morro Bay
Santa Barbara (limited camping options there, however)
Jalama Beach (we've been there but never camped there, lots of people really love camping there.)
Some places I've always wanted to go are California Hot Springs and also Mono Hot Springs.
We like to dry camp in the summer and tend to prefer rustic settings, the beach, & hiking.
If you want to get reservations at any of the CA state parks at the beach, you will need to be on the computer(s) at 8 AM sharp, have your campsites researched as to which ones you will fit into all ready to reserve and your finger hovering over the "book site" button.
Sounds like you will have a great trip - have fun, wherever you end up! CA has so many great camping spots....