My parents retired to NW Arkansas and I tried to find the cheapest way to fly there for several years. Unfortunately I didn't find a really cheap solution.
My best guess would be XNA, TUL or FSM. The closest to you would be XNA (about 100 miles). I flew into XNA a couple of times, it was the closest to my folks and they used to have a number of flights daily on mainline airlines (AA, UA, DL).