Definitely get a car! A highlight of our stay there was driving up into Kentucky to Mammoth Caves Nat'l Park. The region also has factory tours where you can see how they make Corvettes, Toyotas, Saturns, Jack Daniels (and other whiskey brands), Louisville Sluggers (baseball bats), stoneware, dairy products, textiles and glassworks. Most of this would require a car.
There are tours from the resort on certain days (so most helpful if you'll be there a full week) to visit some of the area's museums and the most famous attractions and music venues. You'd be greatly limited on when and where you visit them. It's good that they offer these for those who cannot drive. But, if you can, get a car.