Sunset State Beach (Watsonville area) has overnight campgrounds, was always one of my favorite spots when I lived in CA.
Mono Lake is different, and there are several nice ones in the Santa Barbara area.
I'm not too familiar with southern/central area but heading just about due east into the Sequoia Nat'l Forest you'll find plenty of beautiful spots. Drive a bit further east into Death Valley and check out some stunning views that look like other planets. And now is the time to go to Death Valley.
Just North of Sequoia Nat'l Forrest you have King's Canyon and Sierra Nat'l Forrest. Lots of the dispersed camping in these areas will start opening up in April (short any serious snow). Some of our favorites are around Shaver Lake / Bald mountain.