I've been coming to Riverside campground fo the past 46 years and I'm 48 years old. I've never taken anyone here who hasn't fallen in love with it.
It's on the north end of Big Sur which is great since you can come from the north or drive through Big Sur to get there (which is beautiful).
There are amazing riverside campsites (some for RV's as well) that have picnic tables and fire rings. There isn't the most privacy, but the campground does a good job of putting trees/bamboo between the sites, so you're not joining them for dinner.
The river is perfect for setting your chair in the river and sipping your beer while you watch the butterflies dance across the river and pine trees.
There are also cabins which are great during those cold spells, but I've always been into camping.
The general store is fantastic. You can buy steaks to grill and has a good selection of beers and wine. You could literally show up with just a tent and nothing to eat and be just fine.
There is also a restaurant that is walking distance which is fantastic in case you want different scenery.