Getting into the beachside State Parks last week of March might be a little tough because that's about the time Spring Break starts here in the San Diego area. State parks include Silver Strand, San Elijo, and South Carlsbad. There is San Onofre, San Mateo, and San Clemente further to the north.
A couple regional parks in the area include Gaujome and Santee Lakes.
As for some of the privates I am aware of, the Chula Vista KOA as already mentioned, Chula Vista RV Resort, Campland on the Bay, and Escondido RV Resort (probably the furthest from the ocean).
Not sure what you mean by LRT so I can't help you there.
Frank