The Atlanta Botanical Garden is located near the Woodruff Arts Center and Piedmont Park, closest to the Arts Center Station on the red/gold rail line. In addition to the gardens themselves, there are regular events, including Cocktails in the Garden, art installations and Sun Trust Concerts in the Botanical Gardens.
If you exit at the Arts Center Station, the only option is to walk 20 minutes to the gardens through Ansley Park. Follow the signs to the 15th Street exit (which is up one level) and turn left on 15th Street after walking through the bus bay. Walk up the hill, cross over Peachtree Street and keep walking through the neighborhood until Piedmont Avenue. Turn left onto Piedmont and walk up to the next stoplight, which will be the entrance to the garden (see map). It is about a 20 minute walk.
If you rather not walk, take a red or gold line train to the Midtown Station and get on bus 27. Tell the driver your destination, or exit at Piedmont Avenue and The Prado (first stoplight after the bus turns on Piedmont Avenue). You can also board the bus at Lindbergh Center, but the bus ride will be longer.