First place that popped into my head is Bankhead National Forest and Sipsey Wilderness Area about two hours due west of Oxford in Alabama. Great hiking and paddling options abound. It's like a little pocket of Appalachia randomly located in northwest Alabama. Awesome waterfalls, cascading streams, even hemlock groves. Fairly isolated, too. If you're unfamiliar, just google some pictures. It's pretty solid stuff.
If you're willing to extend your range to four hours, you'd open up a couple of other options, like Walls of Jericho, a natural area along the TN/AL border between Huntsville and Chattanooga, and Cheaha St. Park and Talladega National Forest just east of Birmingham. All three of those would offer stellar hiking opportunities, with Walls of Jericho being more like Sipsey (waterfalls, cove forests, funky rock formations, etc.) and Cheaha and Talladega offering mountain hiking with over 1,000' of prominence. (The elevations of the mountains range from 2,000' to 2,500'.)
Good luck with the trip.