Budget
Kagoshima Little Asia Guest House
A 1-minute walk from Kagoshima-Chuo station take the west exit (è¥¿å£ towards the buses, and walk straight). Free internet, laundry with detergent, guest kitchen, air-conditioning, and TV, ï¿¥280 dinner, weekly and monthly rental available at discount. Both owners speak very good English. Has a consistent run of bad reviews on HostelWorld.
Sakurajima Youth Hostel
TEL +81 99 2932150. If you want to stay overnight on the Sakurajima island, the youth hostel is practically your only budget option. A bed in the dorm will cost you ¥2650 and includes the usage of the hot bath they have downstairs. Note, when I visited in June 2007 the bath was very much out of order.
Nakazono Ryokan
Near the City Hall and close to the ferry terminals. Free WiFi. Free hot tea. Comfy couches. A pleasant place to stay and has a helpful manager.
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.
Asahi Business Hotel
Small and old-fashioned rooms but include TV and shower.