Mid-late June. Im planning a backpacking trip to KY/TN to see them!
Hiked about 35 miles over 4 days, longest day was 14.2...that kicked my ass. Also made me think I should get some mid or high top hiking boots with stronger soles for rough terrain.
I have a pair of Merrell hiking shoes which are great for easy to moderate trails, but on the rocky trails I felt every single rock jabbing my foot, and my ankles were killing me.
I use trail runners; work great!