Outside Charleston’s historic districts, Mount Pleasant is the best residential neighborhood for a run. It’s a large network of quiet, winding streets, with a nice tree canopy and a mix of older and newer homes. The neighborhood is located 10 miles east of downtown. Note that many of the roads don’t have sidewalks, but they’re generally traffic-free.
Given the geography of the neighborhood, we recommend creating your own run. A good starting point is at the Towne Center (basically an outdoor mall), and enjoy running on the roads north of Hwy 17. It’s a lot of winding around shorter, curvy streets, and ~2.5 miles to Boone Hall Plantation and Gardens — make sure you run on the moss-draped 3/4 mile Oak Ave.
Another good spot for a run in north Mount Pleasant is Laurel Hill County Park, a spacious park in the northern part of the neighborhood, with 1-2 miles of paths. You could park there, run the park, and then run on the residential streets south of there and east of Hwy 41. Palmetto Islands County Park is another good spot in the area for a run. There are waterside nature trails. Unfortunately, the approach to the park is on a busier road lacking a shoulder.