Kagoshima is a historical city watched over by the looming bulk of Sakurajima (桜島), an active volcano that regularly dumps ash over the city and erupts a bit every now and then to remind people it's still there. The home of near-mythical samurai hero Saigo Takamori (see History), it's full of sites related to the Satsuma Rebellion.
Kagoshima's Airport (KOJ) 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.
Kagoshima is the southernmost city on Japan's extensive bullet train network. Services terminate at Kagoshima's main rail station, Kagoshima-Chuō (鹿児島中央).
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. Consider buying the JR Kyuushu Rail Pass , the cost for 3 days is 14,440 and will cover all usage of JR trains in kyuushu including Shinkansen. Even if you are just making a round trip from Fukuoka to Kagoshima using Shinkansen, the Kyuushu Rail Pass will save you (¥5000).
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 (鹿児島駅) and Kagoshima-Chuō (鹿児島中央駅). 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-Chuō station is likely where you'll be travelling to and from. Don't confuse them!
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 train the next morning to continue the journey. With a Japan Rail Pass, a connection to a Sakura at Okayama will get you to Kagoshima at around 10:50 AM. Without a Rail Pass you can connect in Okayama to a Mizuho that gets to Kagoshima by 9:45 AM.
Rail Pass holders must pay the lodging charge on the Tokyo-Okayama segment; the rest of the trip by Hikari and Sakura is covered under the pass. Lodging charges currently range from ¥9450 for a B solo to ¥10500 for a B single, to ¥16500 for an A single deluxe. If you really want to travel on the cheap side, ¥3660 gets you your own floor space... literally, you sleep on the floor.
Overnight by train with rest stop
Perhaps the best overnight train option - especially those using a Japan Rail Pass - is to split up the journey, stopping at an intermediate destination en-route in order to sleep somewhere. The cost incurred will only be for the hotel room; the Rail Pass covers your transportation. This is a good way to travel overnight, especially if you are able to find cheap accomodations, such as a business hotel. Yes, it may be a little hectic, and it might require some research, but this method carries two significant advantages: location and money. You will more than likely find good accomodations very close to a main train station in a smaller city, compared to a big city such as Tokyo, and it will more than likely be cheaper than hotels found in big cities. You could use the money you save to forward some of your luggage to Kagoshima using a Kurineko luggage delivery service and take an overnight bag with you, which will make the journey easier.
As of March 2012, here is one way you could go about this from Tokyo: at 7 PM, leave for Himeji by taking the Hikari train and changing to a Kodama service at Shin-Osaka station. Once in Himeji (arriving around 11 PM) you can take a rest at Himeji's Toyoko Inn which costs as low as ¥5230 for a single room or ¥2990 double occupancy. At 6:54 AM the next morning, board the first bullet train of the day, a Sakura service, and you will get to Kagoshima at around 10:50 AM. This trip takes longer than taking the overnight train and bullet train connection as described above, but it is cheaper; you only have to pay for the hotel room, complete with your own toilet and shower.
Various overnight bus services are available to Kagoshima from Osaka and Kobe (~¥10000 one way; ~¥21000 round-trip). Tickets for Osaka and Kyoto can be bought from Willer Express's English site  for around ¥7800 each way. Daytime and nighttime buses also run from Fukuoka (yen 5400 one way; 4 hours) and Oita. There are day buses from Kumamoto for about ¥3600; 3 1/2 hours.
Kagoshima is one of Japan's most busy ferry terminals, with a multitude of ferries connecting mainland Japan to its southern islands. For the Okinawan archipelago there are several routes towards Naha which stop on different islands along the way. Operators include Matrix Line  and A Line ferry  - expect the full journey towards Naha to take around 25 hours, although you can stop halfway through in the Amami Islands. Towards the world heritage site of Yakushima and the island of Tanegashima near Kyushu you can opt for either Orita Kisen  (4 hrs, yen 4000) or the Toppy  hydrofoils completing the journey in just under 2 hours (yen 7000). Finally, for the Tokara Islands, the municipality  operates 2 weekly ferries plying the route in around 7 hours (Yen 6000).
Streetcars are a convenient way to get around Kagoshima city. Both lines 1 and 2 can be boarded at the Kagoshima station; only line 1 runs by Kagoshima-chuo. Board the tram from the back door, and pay the ¥170 per ride fee when exiting the front door. If you don't have exact change, the fare machine can make change, but it is polite to get your change during the ride, so as to not hold people up when at your final stop. Pasmo cannot be used either. Streetcar signage varies by the age of the streetcar; some have electronic signs that indicate the stop, but many do not. Streetcar information and a route map are available from www.synapse.ne.jp.
The ferry between volcanic island of Sakurajima and Kagoshima harbor operates frequently and around the clock. The boat ride will take about fifteen minutes.
Given Kagoshima's relatively small size and straighforward layout, buses (¥150) are less confusing than in larger Japanese cities.
If you plan to make Kagoshima a base for multiple trips, or make Kagoshima a stop on a trip throughout Kyushu, then a 5-day Kyushu rail pass may be the best option. If you are travelling from Tokyo or farther via train, then a 7-day Japan Rail pass is about the same price as a one-way shinkansen ticket from Tokyo to Kagoshima. Both of these passes have extensive limitations; be sure to review terms and purchase your pass before entering Japan.
Tenmonkan shopping arcade has a plethora of shops, where you can satisfy your consuming needs.
In Kagoshima, the most common way to drink shochu is mixed with hot water, or oyu-wari. This releases the fragrance of the shochu, and also reduces the alcohol content to be on-par with wine. Because Kagoshima is the center of manufacture, many factories offer tours and have small shops for tasting and purchasing the locally made shochu.
If you're looking for inexpensive accommodation, the tourist information in the Kagoshima station can hand you a leaflet, where they have listed all the inexpensive options in Kagoshima. They can also check availability and book the accommodation for you.