Everyone visiting the Smokies does the mountains. Far fewer do the water, and that is a mistake. Douglas Lake is about 20 minutes north of Sevierville, and on a hot week in July it is the best-value day you will have.
It is a big TVA reservoir with 500-odd miles of shoreline, which means there is always a quiet corner. Rent a pontoon for the day and you have your own patch of water for swimming, tubing and lunch. If you would rather not spend the money, the shoreline near Douglas Dam is free, easy to reach and shallow enough that little ones can paddle while somebody fishes. Bald eagles nest in the area and are seen often enough to be worth watching for.
Best time is late May through early September, when levels are high and the water is warm. Levels drop through fall and winter, which changes the shoreline a lot — worth checking before you plan a boat day.
Take a cooler, take shade, and go early. The light on the water in the last hour before sunset is the bit people remember.