Cape Canaveral National Seashore
This is one of those wild places hemmed in by civilization, most notably the Kennedy Space Center, which lies just to the south. (It may be the only national park with sections periodically closed because of space launches!)
Even so, several boat launches provide access, and much of the park is surprisingly secluded and quiet, home to alligator, egret, and loggerhead turtle. Limited camping is available along some beaches and year-round on designated islands. Check with headquarters for dates and permit information.
Don't be overly put off by the civilized surroundings. Much of this park is wild and primitive. Besides, who knows, you might see the space shuttle land from your campsite!
Details mentioned in this article were accurate at the time of publication