Spring is always good. (with green leaves-budding flowers-flowering trees)
At Elkmont along the Little River
Upper Spruce Falls (by the Institute)
Rich Mountain road-overlook (turn off in Cades Cove). Great view of the valley from this road
Many scenes along the Little River road between Cades Cove and the Visitors Center.
Of course the regular spots Clingman's Dome, Cades Cove, Morton Overlook, many turnouts on the road from Gatlinburg to Clingman's Dome.
Waterfalls, Waterfalls & more waterfalls.
Roaring Fork Rd. (start in Gatlinburg) best in the spring when the trees are blooming (Dogwoods, Redbuds etc.)
did I mention Waterfalls?
For the more adventurous there is a backwoods road that you enter from the loop rd in Cades Cove (sorry can't remember the rd) Gravel, sometimes closed in bad weather. Nice isolated areas
Great morning/sunrise opportunities on the Parkway (near Townsend, Tn)
Really good when the fog is present. Good in spring and sometimes excellent in the Fall