From Shin-Osaka to Wakayama: Take JR Kinokuni line Limited express (about 1 hour)
From Shin-Osaka Station, 2 hours by JR Hanwa-kisei Honsen Line Express Train to Shirahama Station. From Shirahama Station, take a bus to Kumano Hongu Taisha, 1 hour 18 minutes.
http://www.pref.wakayama.lg.jp/english/c…