Both have plenty of outdoor activities (whitewater rafting, hiking the AT or any of the other hundreds of nearby trails, ziplining, kayaking and canoeing, paddleboarding, Chimney Rock, waterfalls and a handful of National Forests, Asheville within an easy drive, etc).

You could try to Sky Valley or Lake Lanier in North Georgia (depending on whether you want mountains or lake watersports and golf). Or rent a beach house on the OBX or in Charleston or in Gulf Shores.