If you are needing to stay close to Pigeon Forge/Gatlinburg you can fish along the road between PF and Gatlinburg also called the "spur". They stock that part of the river during the summer months and there is usually some decent fishing with easy access along that stretch. If you get into the mountains you can drive from GB over to townsend and stop anywhere along the way that you see water. If you fish in Gatlinburg make sure you get your day permit before fishing.
You can also search this forum to see what other people have said in the past for fishing spots.
As for flies to use... I would use what Byron recommends on the fishing report. You can also call the shop once your down here, better yet drive over to Townsend and check out the shop and give them your support. They will be able to help you with what the fish are rising to.
I hope this helps. Good luck with your trip and make sure you post some pictures of your catch.