Freedom Park is one of Atlanta’s large city parks. The heart of Freedom Park is the Carter Center, which is well worth a visit. The area is very green and shaded. There are pleasant running/biking trails heading east from Parkway Dr. to Chandler Park, south toward Inman. I have two suggested routes for this area: the entire 2.5 mile (one-way) Freedom Parkway Trail, from the Martin Luther King National Historic Site to the Carter Library and some of the trails lining Freedom Parkway. Another option is a 3.6 mile loop, starting at the Carter Library, and running the trails of Freedom Park to Chandler Park. A very pleasant, green run.
Another nice add-on is Olmsted Linear Park, a series of small parks just north in Druid Hills. A paved path follows Rt. 78 for nearly 2 miles through several parks: Springdale, Dellwood, Shady Side, and Deepdene. Can also be made into part of a loop incorporating the Freedom Park Trail.