Anchor Down is a great campground, but doesn't really sound like what the OP is looking for. OP, just above the dam and across the river from Anchor Down is Douglas Dam Campground (also called the Headwater Campgrounds). Just under the dam and right on the water is the Douglas Tailwater Campgrounds.
They both look right up your alley, wooded and less commercial and both offer water and electric. We really liked how Tailwater looked, its literally on the water a little ways below the dam.
https://www.tennesseerivervalleygeotourism.org/content/douglas-dam-headwater-and-tailwater-campgrounds/ten33694afd6f5839141
For those considering Anchor Down, it is really gorgeous. Its up on a hill, so you have to walk down a path to get to the water. Really nice pool with a pretty good snack bar, very pretty campground with great views and nice pads. Main office and restrooms were very nice. Not a lot of trees, it gets toasty in August when we went. We loved it and will go back again (8 hour drive though). Pretty easy access to Pigeon Forge and Gatlinburg too.
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