One of my favorite places to run - the Moses Cone park is located between the Blue
Ridge Parkway (about mile 290) and US 221, just south of Blowing Rock.
The park was an estate owned by Moses Cone, who built about 25 miles of horse carriage trails as a present to his wife. The trails are well-graded, and mostly are crushed gravel. Some (like the short loop around Bass Lake) are flat and frequently used by walkers. Others are less often used by walkers. My favorite run is to start at the lake, run through the Maze, then up the mountain to the manor house. Coming down the mountain back to the lake is special. Although this is in the NC mountains, most trails are not too steep (as these were designed to be carriage trails) but there are some decent climbs.
There is no entrance fee - parking is available at the Bass Lake entrance on US 221, or at the Manor House on the BRP (which is worth a visit anyway). Maps are available at the Manor House, but there is a display map at the lake as well.