Billy Graham Library, especially in the spring. It's beautiful, interesting, and surprisingly well done, especially after the cow stops singing.
4. Try to see the state bird, the cardinal, on a blooming dogwood tree (it's the state flower).
Pilot Mountain, go a few miles north to the town of Mayberry... or rather, Mount Airy. Take a tour of the town in a squad car, or have a sandwich at Leon's. A few miles west of town, visit Scoops Ice Cream and wander through the sculpture garden.
Smoky Mountain National Park and take a walk in the woods. It's free, but watch out for bears.