We stayed 2 nights at San Pedro, using it as a base camp to explore Amistad National Recreation Area. It's very close to the Spur 454 boat ramp, which we used to launch our kayak. You can also get over Diablo East, Governor's Landing, and the Figueroa trail for good hiking by driving maybe 10 minutes. 

The non-tent sites all have covered picnic tables with a concrete pad and charcoal grill. There are quite a few pit toilets dispersed amongst the sites. There doesn't seem to be anyway to get down closer to the lake from this campground. 

When we were there, we saw 4 - 5 other campers in the campground and everyone setup spaced apart. We heard lots of coyotes in the distance just after sunset.