There is an road just south of 57th St off Lake Shore Dr called Science Dr which provides access to the parking lot. After you turn on Science Dr, veer left to the larger parking area (away from the museum) and find a spot at the western end. Cross the bridge on foot and walk the short distance to the gardens.
Yet another image from my Osaka Gardens collection. Albeit, this is the only image out the group with an HDR treatment. While not being too excessive, I think it adds to emphasize the tranquility and solitude of the early morning.