Lundgren Island is on the St Johns River just South of Astor. I camped there several times in the 1970's and 80's, but not recently. (Since this information is so dated, you might want to do a day trip to the island before committing to an overnight.)
There's a decent wading/swimming area, and room for several tents. On weekends there's far too much boat traffic for decent skinny dipping, and picnickers and waterskiers often land on the island. These weekend warriors typically left mountains of trash behind in the past, so don't be surprised.
On weekdays however, naturist camping and skinny dipping here was always quite feasible.
An interesting thing about this island is that between the island and the East riverbank (about 500 feet north of the island), an old steam powered riverboat ran aground long ago, and it's remains are still visible in the water.
Another interesting feature here is the frequent nighttime passage of oil barges. These barges are pushed by tugboats with locomotive engines. They are well equipped with navigation lights, and the combined effect is like hearing a train roar past at a snail's pace while a UFO hovers past, low over the water!
The first time I camped here, we had left the sterns of the canoes in the water, only pulling the bows up onto the beach. When I heard a barge coming, I was concerned about it's wake washing over the canoes. I went outside to watch (in my 'pajamas' - a.k.a. Birthday suit), ready to drag the canoes in further if necessary.
As the tugboat passed (maybe 75 feet away), a side-mounted spotlight came on, panning around the beach and quickly settling on me. I fought the panicked urge to run and hide, and instead just waved. (After all, they had already seen me 'in all my glory'.) After a couple of seconds, the light went out, and a front spotlight came on, sweeping the river ahead of the barge as it continued on downriver. (They had a story to tell back home, I guess.)
The wake was minimal, and I didn't need to move the canoes.
