What I think you want is not really available in the San Diego/soCal area, at least in the US.
I live in San Diego and have camped all over soCal and Baja (dozens of trips). Baja is the ticket if you want to camp on the beach outside of a campground anywhere near here. The Lost Coast is great, but it is not near San Diego. Pismo is great too, but a long drive north.
In SD County you essentially have San Elijo, San Onofre, and So Carlsbad Campgrounds (as noted above; all north of the City of San Diego. San Onofre is near the town San Clemente very near the Orange County/San Diego County line). Nice, but all relatively crowded, and probably tough to get a spot this time of year. Not a place to hang out and relax, IMO. Nevertheless, my guess is San Onofre is the closest thing to what you want on the US side of the border.
In Baja I can suggest camping south El Rosario on the Pacific side, or south of San Felipe (as noted above) on the Sea or Cortez side. It normally takes a little research to do this right... I used to camp in some areas on the Pacific coast between Ensenada and El Rosario (these are substantially closer to San Diego), but not any more. PM me if you want some more data.