If we drive to those cities, could we return to the 鹿兒島city at the same day?
I am going to 鹿兒島 for 6 days in June. I would go to Izumi for 2 days (mostly take bus... or is it better to drive there too?) and then I haven't planned where to do yet. But the cites you mentioned would be in my list too.
At first I would like to go to some islands for the forest and mountain but the weather would be too bad in June.