Occoneechee State Park in Virginia is just an hour drive west near Clarksville. The park offers ~3 miles of hiking specific trails and an additional 17 miles of multi-use trail. Note there is an entrance fee to the park.
Occoneechee State Park: https://goo.gl/maps/a7ooFgVEnu1FEjgq7
Note: The park is OPEN during COVID-19 (including restrooms).