Max Patch is a bald mountain located on the NC/TN border offering 360 degree panoramas. It can be reached through a variety of trails or you can simply drive to it via NC road 148. (Take exit 7 from I40.) It also offers plenty of good camping spots.
The Appalachian Trail runs across the top of Max Patch.
Click image to see larger view of 360 Pan of Max Patch.
Here are two of the hiking options:
From Brown Gap via the AT
To Lemon Gap
There's a nice loop that can be hiked from Brown Gap via the Cherry Creek Trail. Pick up a copy of Appalachian Trail maps #3 & #4 or National Geographic Topo map #782 to find other options.
Distance from downtown Greenville: 105 Miles
View Larger Map