Kagoshima is located in the deep southern Kyūshū, therefore reaching it by plane from Tōkyō and western Japan might be the best way. There is a bus service between Kagoshima city and its airport, and the fare is 1.200 yen as of 2015.
・By Shinkansen (bullet train)
From Ōsaka and eastern Japan the Shinkansen can be a good option. The “Mizuho” Shinkansen travels directly from Shin-Ōsaka to Kagoshima-Chuo Station in 4 and a half hours. The fare for a one-way trip is about 22.000 yen.
For those who come from other areas of Kyūshū the Shinkansen is more practical than travelling by plane. It takes 100 minutes to reach Kagoshima from Hakata Station (Fukuoka), and the ticket costs approximately 10.000 yen.
If you are also planning a retour by Shinkansen there is the so-called “two tickets” discount service. To use the service you have to travel back within a month from the departure.
We remember you that if you are traveling with the Japan Rail Pass, you may not ride the Mizuho Shinkansen, but you can take the Sakura service, either linking Shin-Osaka with Kagoshima-Chuo, although it takes about 30 more minutes. Also, if you are a student living in Japan for a limited time, you can get the Ryūgakusei Pass Kyūshū, at less that 15.000 yen, which is really convenient!
There is a intercity express bus between Kagoshima and the metropolitan area of Ōsaka.
The cost is pretty low, compared to Shinkansen and air, and by traveling overnight, you can visit the city from the early morning, and this can be advantageous to save on time and accommodation fees.
Kyushu has an extensive network of intercity bus, so if you are already in Kyushu, you can reach Kagoshima easily from every main city. For example, a ride from Fukuoka takes about 4 hours. There are many rides, even 2 or more bus per hour (depending on the time zone). There is also a night-bus service from Fukuoka.
To get to your final destination, Sakurajima, you just have to reach the ferry terminal, close to Kagoshima Station.