You can take time to visit Bald Rock Heritage Preserve during your travels to Cleveland. While you're in the area, wander around the natural setting.
If you like spending time outside, why not spend the afternoon at Jones Gap State Park, a park located 21 mi (33.8 km) from the centre of Greenville - Spartanburg. Want to stretch your legs some more? Head to Caesars Head State Park and Mountain Bridge Wilderness Area, both nearby.