Sorry for the late reply. We tried to do two things/scenic spots max each day so our itinerary is quite simple
We went to 神話之里公園 in 霧島 quite worth a visit.
We also drove to 櫻島 and like the other poster said it's much easier driving and the experience of taking the car on the ferry was quite special.
The people are really friendly and I remember the old ladies on 櫻島 near where they sell souvenirs gave us some oranges/ mandarins for free tasting.
By the way I was reading the newspaper today and saw some info per attached