Road runners in the Asheville area are blessed with a wide variety of excellent options. Beaver Lake provides a quick and pleasant run around a pretty urban lake in a residential area. No hills, just a few gentle slopes on the gravel path. Park in the Bird Sanctuary parking lot and exit to the left to pick up the path. It will briefly take you onto the sidewalk on Merrimon Avenue, but from there, you'll turn back in to the left to the Beaver Lake path.
If you're anywhere south in Asheville, Fletcher Community Park is a nice, easy run on smooth gravel travels. The smooth, 4-mile-long greenway travels alongside Cane Creek and there are also other shorter trails in the 70-acre park. There are several shady sections along the trail, which is rarely crowded.
In the shadows of the Great Smoky Mountains and the Plott Balsam Range lies the beautiful Lake Junaluska. Circumnavigating the lake is a 2.6 mile trail that is adorned with historical buildings and lavish landscaping. Whether you are looking for a casual stroll or an intense run Lake Junaluska provides a striking venue to exercise amongst the mountains.