If you end up headed this way, University of Tennessee, Knoxville, while its not "next door" (20-60 min by car) to Great Smoky Mountain National Park also has in the eastern half of the state

more than nine lakes (one across the road from campus)
national recreation/parks (Big South Fork & Cumberland Gap)
state parks (Fall Creek Falls, Roan Mountain, Cumberland Mountain, Warrior's Path)
national forests (Nantahala & Cherokee)

These are just the ones that I can name off the top of my head.

Knoxville/Knox County is in the process of developing greenways in parts of town. There is also Ijams Nature Center (80acre park that started as a 20 acre bird sanctuary) 3 miles southeast of campus w/ some trails.