You must try the Arkansas state parks. Petit Jean, Mt. Nebo, and Devils Den are my favorites. The National Forests in Arkansas also has nice trails and camping areas in mountainous terrain.
I have been looking really hard at Buffalo River NP. Might be a late May trip. Not atrociously hot yet but also warm enough for water fun.
I spent a few days at the end of October hiking Amacalola State Park in north Georgia. The south end of the Appalachian Trail starts there. The Falls were beautiful as were the trees. Lots of trails to choose from both in terms of length and difficulty.
That is another trip I am looking into... There are some nice cabins in the Blue Ridge area. I would love to eventually do a section of the AT.
I pretty sure that Tunica Hills is not an overnight camp site for what its worth. Lake Fausse Point is an excellent primitive camp site. It has some awesome pack and paddle areas. I want to say that #5 is my favorite. Very large area and surrounded by water. http://en.wikipedia.org/wiki/Lake_Fausse_Pointe_State_Park
As I explained many moons ago: "I don't think that there are any *official* camping areas there... ...ya just gotta kinda "rough it"..." http://www.tigerfan.com/threads/camping.24802/page-6#post-275901
The Clarks Creek area is too busy with day hikers to get any kind of wilderness camping experience and it's not permitted anyway. There is a nearby wildlife management area where you can rough it, but only out of hunting season and you must have a permit and a wildlife stamp even if you are not hunting or be ticketed by game wardens who see your cars and will find you. Honestly, the Tunica hills are extremely hard to hike through cross country with really steep ravines by the hundreds and dense undergrowth. But there are some hiking trails and some private campgrounds nearby, some with tent-only areas. I normally consider Tunica to be a day hiking area.