Where I live, there's islands which are not owned by anyone in the rivers. (Check your county's GIS map for which ones) You can just go camp on those, no problem.
In the Great lakes, there's islands which offer ferries to go camping backcountry-style. I highly recommend visiting North Manitou Island, which is an abandoned farming/logging/vacation community where you can see the ruins of old houses and homesteads. There's also a south island which I haven't visited, which is a little less wild. Ferry runs from Leland, MI. Probably one of the best camping trips I've ever taken, beautiful.
My advice: Download Google Earth Pro (now free!) and just scroll around until you find something. Then search for info about said island, and see if anyone owns it (if not, you can probably just find a way to get there and camp).
As always: Leave the place cleaner than you found it!