There is a very nice garden center near Crossville. It's just off I-40 east of Crossville and visible from the highway. I'm pretty sure it is at the next exit going east from Exit 317.

At the University of Tennesse in Knoxville, the Ag Campus' trial garden, next to the river.
The National Park at South Fork, for wilderness.
Are you interested in Native Plant nurseries?
A longer drive would the the Rhododendrons at Roan Mountain State Park.