By train
Wakayama can be accessed on the JR Hanwa Line and the private Nankai Main Line, both of which run south from Osaka City.
JR Wakayama station can be reached by Limited Express trains from Shin-Osaka station, departing every hour. The Kuroshio, Super Kuroshio or Ocean Arrow run from Shin-Osaka to Wakayama in one hour at a cost of ¥2660. From Tennoji the run takes about 45 minutes ¥2280. There are also five daily Limited Express departures from Kyoto 90 minutes, ¥3660. From major stations on the Osaka Loop Line, regular Rapid trains run to Wakayama every 20 minutes: look for the Kishiyuji Rapid ç´å·è·¯å¿«é. It takes about 90 minutes from Osaka ¥1210 and one hour from Tennoji ¥830. Be sure that you are in the correct car, as part of the train splits off to Kansai International Airport.
The above trains are free with the Japan Rail Pass.
Nankai Railway has two stations: The main station, located marginally closer to the castle than JR, is called Wakayamashi. The other station, Wakayamako, is adjacent to the Nankai Ferry terminal where ships operate to/from Tokushima. Wakayamashi is served by Nankai Railway's Limited Express train, appropriately called the Southern. Trains depart every 30 minutes from Nankai Namba station, running to Wakayamashi in about one hour at a cost of ¥1390. Select trains continue on to Wakayamako, five more minutes away. By regular train it takes 75-90 minutes to reach Wakayamashi with a change of trains required enroute, at a cost of ¥890. All trains pick up and discharge at Shin-Imamiya station, which is a stop on the JR Osaka Loop Line.
By bus
An overnight bus service operated by Narita Kuko Kotsu runs daily from Keisei-Ueno station in Tokyo and Yokohama station in Kanagawa to JR Wakayama and Nankai Wakayamashi stations. The one-way cost is ¥9000 from Ueno and ¥8600 from Yokohama.