I've been to Playalinda Beach which is part of the Cape Canaveral National Seashore in the Titusville/Cocoa Beach area. Yez, I believe it is actually owned by the government, lol. There's been some minor controversy about it over the years, but mostly it's been left alone. You have to walk quite a ways down the beach to get to the nude section.
It's been many years since I went, but I loved it. I find it much preferable to sitting around in a wet bathing suit. And the feeling is quite glorious - both in and out of the water. Liberating.