Jones Gap is great place for a picnic, a hike or primitive camping. 
The Jones Gap Trail runs along the Upper Saluda River which is a beautiful river and home to brook and rainbow trout. It leads to a small waterfall as well as to a number of other more difficult trails.
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.
Click image to see larger view of 360 Pan of Max Patch.
It also has some great trails of varying degrees of difficulty. 
It has two RV/tent campgrounds, as well as primitive walk-in campsites and some very nice (although rustic) cabins for rent. One of the great things about the cabins is that they have large stone fireplaces that (unlike many cabins) burn real wood. 
Distance from downtown Greenville: 32 miles.
Over the last decade, the Blue Ridge Mountain range has quietly become a home to dozens and dozens of wineries. The highest concentration of Carolina vineyards can be found in the Yadkin Valley. Sadly though most of these east coast wines leave much to be desired and in addition are over-priced. Knowing this, my wife and I didn't expect much when we stumbled across the Victoria Valley Vineyards, but we were pleasantly surprised. We tasted 12 different wines and found them all to be quite good.
