At Exit 5 in Bristol, VA, (exits are 7, 5, 3, 1 and then 74 in TN) there is Sugar Hollow Park, a locality owned campground that has some sites with water/electric. It's $15/night for electric sites, $12 for non-electric.
At Exit 57B in TN, another 20 miles down the road, about 3 miles off of the interstate is Warriors' Path SP in TN. Lots of sites.
Outside of Marion, VA at Exit 47 is Hungry Mother SP. It is about 5 miles off the interstate.
In Virginia, SP prices are $30/night and TN SP are $20/night.
If I can help more, just hit me a PM. This is close to home, so I know many of the area campgrounds.
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