I've heard of several campsites like this in Northern California, but I'll let you in on this secret because it's likely that you'll be nearby it this summer anyway.
There's a Lake Tahoe campsite in Emerald Bay that requires you to take a boat to get there because it's so remote. Depending on where you launch from, it could take an hour or two to get there by kayak.
Only In Your State shares the location on Google Maps here.
Starting Memorial Day Weekend, the 20 campsites are available on a first come first served basis. Only In Your State says that campsites #1, #21, and #22 all come with their own beach!
Read more about the campsite and see photos here.