From my personal bucket list, meaning I want to go but have not done so yet...
Berryessa Snow Mountain National Monument
This is north of you. Probably pretty primitive.
https://www.blm.gov/programs/national-conservation-lands/california/berryessa-snow-mountain-national-monumentFrom my been-there-liked-it list:
San Luis Reservoir State Recreation Area
South of you near Los Banos.
A variety of camping areas, ranging from primitive first-come-first-served (Medeiros, where I always stay) to full hookups with lake views.
https://www.parks.ca.gov/?page_id=30712
