Tweetsie Railroad, near Boone, NC. Another from the film days. As noted at Wikipedia: Tweetsie Railroad is a family oriented railroad and Wild West theme park located between Boone and Blowing Rock, North Carolina. In addition to a 3-mile ride aboard an authentic steam locomotive, the park features amusement rides and other attractions geared towards families with children.
Tweetsie is one of those places that went to as a child, and then took my kids decades later. I'm not sure exactly when this was, but it was before my son was born. Probably '96 or '97. Not as impressive as Disney, nor even 6 Flags. Or even Holiday World for that matter. But I enjoyed it just fine.