Kagoshima Airport is not in the city but in Mizobe in Kirishima. That makes a round near the airport easy on an arrival or departure day, and the city is about forty minutes away by limousine bus.
Many layouts look out toward Sakurajima or use the volcanic terrain. Ibusuki and Kirishima hot springs sit to the south and north respectively, so which onsen you book changes which courses are practical.
Being in southern Kyushu, winter rounds are usually possible. On days when Sakurajima drops ash, however, operations and course conditions can change, and in summer an early tee time helps.
Comparing a Japanese tee time on the headline green fee alone tends to produce a different number at the counter. Confirm whether cart, caddie or self play, lunch, locker and the local golf tax are included, then check rental clubs or shoes, minimum player counts, two-player supplements, payment method and whether overseas visitors can book. Clubs may also specify check-in times, dress codes and bathing etiquette, so submit player names accurately.
Landing, playing a round near Mizobe and staying at a Kirishima or Ibusuki onsen, then pairing a city-area eighteen with Sakurajima sightseeing on day two, keeps the driving to a minimum.