Camp and fish in the same spot is a tough one. Most of our lakes don't have camping. You could check in to Del Valle but my long lost recollection is that you have to stop fishing at 10pm. They do have camping.

Coyote has camping and you can fish real close but that lake is not known for catfish. I've seen guys get bullhead there but never cats.

Pinto has camping. Don't know about fishing at night or presence of catfish.

There's always the Delta. Tower Park or any number of places to camp. You might very well get some cats. Camping near Russos is a possibility though don't know the shore fishing options there. Sugar Barge maybe?

If you just want big cats without camping, the places to go are Los Vaqueros or San Pablo. Both have big channel cats. Vaqueros produces 20lb fish just about every week.

Try the big map here to explore around more:
http://www.calfishing.com/loc/bigmap.html