I am sorry for replying late. I am a resident of Kagoshima for more than 40 years so I think I know about Kagoshima more than most of persons here. But this does not make me the best guide for Kagoshima. Maybe I am too used to the typical sightseeing spots. It's like I don't prefer Tokyo since I have been too many times in Tokyo. But I will try.
Sakurajima is definitely the most important spots in Kagoshima. The mountain by itself is not so spectacular, but itf active volcano and is very close to the relatively big city, and further you can see it beyond the city and strait. This is quite unique view. As Who? wrote, Shiroyama park is the best spot for seeing Sakurajima.
Other than that Kagoshima city by itself has not so many things to see. Itfs because of the WWII.
You can visit the mountain. Yunohira observatory which is 8 km from Sakurajima port, 373 m high. You canft see the crater, but can see the huge body of the mountain.
Other than that Kagoshima city by it self has not so many things to see. Itfs because of the WWII. By the way do you know about 200 years ago, Japan is not a single country but an alliance of small countries? Kagoshima is one of them and in 1863 it fought against the Great Britain.
https://en.wikipedia.org/wiki/Bombardment_of_KagoshimaApart from Sakurajima, there are so many volcanoes in Kagoshima. Take a look at Google map and you will find many circular lakes/ponds. Many of them are crater lake.
https://www.google.com/maps/@31.9191993,130.8574763,11187m/data=!3m1!1...Well two days enough? I donft know. But I can arrange 2 day tour including Sakurajima, Kagoshima city and some side trips to somewhere depending on your interest.
After I joined the Japanguide, I had honor to drive 4 foreign guests around Kagoshima. Of course I drove my Japanese friends several times.
Below are the places I took them. Of course they are my favorite places in Kagoshima.
Shiroyama park.
Ferry to Sakurajima and Yunohira observatory.
Ibusuki gskylineh driveway and Chiran samurai village.
Kasasa fishery village/port.
Sengan-en garden.
Ebino plateau and the volcanoes around. Actually Ebino Plateau is in Miyazaki prefecture though.
In the past Japanguide allowed us to communicate personally, but it seems to be no means on the Japanguide. I think showing my e-mail address is prohibited. If you would like to communicate with me personally there may be some methods.
Enjoy your planning and trip in Japan (especially Kagoshima)!