By plane
Kagoshima's Airport is one hour away from Kagoshima's main train station by Bus (�1200). JAL and ANA offer flights into Kagoshima from several major cities in Japan. Kagoshima Airport is also the starting point for many flights to Okinawa and the surrounding islands.
By train
Kagoshima is the southernmost city on Japan's extensive bullet train network. Services terminate at Kagoshima's main rail station, Kagoshima-Chu?.
Kyushu Shinkansen trains run several times per hour from Hakata Station in Fukuoka, taking as little as 80 minutes at a cost of �10,170. If you have a Japan Rail Pass you can use Kyushu Shinkansen services at no charge, with the exception of Mizuho trains.
Sakura and Mizuho trains connect Kagoshima with stations north and east on the San'yo Shinkansen network. Using the Sakura, Hiroshima is 2 hr 40 min away (�17200), Okayama 3 hr 20 min (�19830) and Osaka 4 hr 10 min (�21300).
From Tokyo, it is possible to travel the full distance of the Tokaido, San'yo and Kyushu shinkansen lines in 7 hours using a combination of Nozomi and Kyushu Shinkansen trains. Japan Rail Pass holders can make a day trip in 8 hours using a combination of Hikari and Sakura/Tsubame services.
Note that Kagoshima has two central stations, Kagoshima and Kagoshima-Chu?. The former is the older station slightly to the north of the city centre, and you're unlikely to use it. The much larger Kagoshima-Chu? station is likely where you'll be travelling to and from. Don't confuse them!
Sleeper Trains
Because all sleeper trains from Tokyo and Kansai to Kyushu have been discontinued, traveling overnight to Kagoshima strictly by train could be a little difficult. Thankfully, trips are easier to make now that the Kyushu Shinkansen is fully operational.
From Tokyo, it is still possible to take an overnight train, the 10 PM Sunrise Seto/Sunrise Izumo, to Okayama where you can connect to a bullet