Just after some thoughts on my itinerary for my 5 nights in Kyushu (will be there in just over 3 weeks time):
Day 1 - Arrive in Nagasaki: check out the Huis ten Bosch & Hollander Slope.
Day 2 - Nagasaki: Visit Peace Park, Atomic Bomb Museum and maybe Glover Park.
Day 3 - Leave early for Kagoshima. Find somewhere for good views of Sakurajima (any ideas?).
Day 4 - Leave for Kumamoto. Check out Kumamoto Castle and Suizen-ji Garden.
Day 5 - Bus tour of Mt Aso (any ideas of companies who provide this?).
Day 6 - Leave for Kobe.
I will have a JR Railpass for travelling.