Kyushu 6 night itinerary check

We're headed to Kyushu for 6 nights! We've traveled to Japan a few times but never made it to the southern island.

We're taking the train from Tokyo and then our plan is to fly out of Kagoshima to Seoul for a few days.

Trying to build an itinerary but have a bit of information overload and have no idea where to stop in the middle of our trip, between Fukoaka and Kagoshima. We like nature, hiking, eating music, really happy with anywhere not too touristy, off the beaten path that connects us to local culture!!  We'll be renting a car in Fukuoka and driving down

• Fukuoka (2 nights) Exploring town, renting bikes, eating 
• not sure where to stop in the middle! (2 nights) 
• Kagoshima (2 nights) – Exploring water-front towns, getting buried in the sand in Ibusuki, ferry to Sakurajima for hiking etc 

Any and all tips are appreciated & thanks in advance!