The Oconee River Greenway runs through several very picturesque areas of Athens, and it is constantly being expanded. It is easily accessible from several different spots in Athens.
From Singletracks: "Two Trailheads, many good spots to jump on. One trailhead on Lexington, right after crossing oconee river, stay on sidewalk, cross lexington, follow signs. Other trailhead at Sandy Creek Nature Center off 441."
http://www.tripleblaze.com/trail.php?c=3&i=2260