Thai Palace in Sevierville is my go-to option there. The food is always fresh and delicious, and any meal can be prepared vegan by adding tofu, because the owner told me they use no fish sauce in their dishes. Plus, it is a local business that serves beautiful food, and it always makes me feel smart avoiding the chains in such a commercial location.
Bistro 109, located in Sevierville's historic downtown is also a nice choice for a more upscale meal. They have a pretty good selection under their vegetarian options, that can easily be made vegan. I travel to/through the area quite often, and I've yet to starve!
Thanks for the suggestions. I've actually eaten at the Thai Palace and you're right that it's really good.