Japan Railways Limited Express operates a train from Kobe to Wakayama every 2 hours. Tickets cost $22 - $27 and the journey takes 58 min.
How to get from Kobe to Wakayama
From Shin-Kobe train to Shin-Osaka then train to Wakayama. 2 h 11 min ¥4880. From Kobe Sannomiya bus to Kansai Airport, train to Izumisano, then train to Wakayamashi. 2 h 20 min ¥2797. From Kobe drive to Wakayama. 1 h 7 min ¥1362.