If you have a few days in Kagoshima then spending one in Kagoshima city, and one visiting Sakurajima Volcano makes a good itinerary. The volcano is still active, and on some days sends smoke over Kagoshima.
To get there take the Sakurajima Ferry. This leaves from Kagoshima Port ever 10-15 minutes for most of the day, and ever 30-60 minutes outside of peak hours. The journey to Sakurajima Port is only 15 minutes. For adults the ferry fee is ¥150 and ¥80 for children and you pay when you reach Sakurajima.
Some of Sakurajima’s sites are located in easy walking distance of the port, but for others (especially the various view points) you’ll either need your own car, or to take the sightseeing bus. There is one bus in the morning and one in the afternoon at 9:40am and 14:20pm departing from Sakurajima Port. The trip lasts two and a quarter hours. The tickets are ¥1700 for adults and ¥850 for children. This was correct as of August 2010, make sure you check the departure times, and cost before you go!
On the bus there is a guide who gives commentary, but all in Japanese. Fortunately if you can read English there is a translated text version of the talking. The guide will tell you which bit he/she is up to at regular intervals.
As the bus takes you round you can see the volcano from various angles. One of the stops is at the Yunohira Observation Point from where you can see the effect the volcano has had on the landscape.
There are two buried Torii gates along the way. Here is one of them that we stopped by.
There are plenty of volcanic rocks formed from past lava flows along the way. Here are some examples.
The bus then drops you back at the ferry port. If you want to nearby visitor centre make sure you plan it in as it closes early (I think 5pm). Between the visitor centre and the sea if the Yogan Nagisa Park Foot Spa. From here you can soak your feet in fresh natural hot spring water. It is free and you can get a good view of the bay while you relax.
There are other attractions on the island if you have more time such as the Sakurajima Dinosaur Park and several hot springs.