You should ride to the top of Mount Unzen. It's very cool. Watch the movie "Silence". It's set there.

You should also check out Mount Aso.

Last year I rode the entire length of Japan from Aomori to Nagasaki in 40 days, including big detours, crossing between the west and east coast multiple times, several mountain summits, and plenty of days off for sightseeing. It seems like a bit of a missed opportunity to spend your 40 days just on the one island.

But of course you will be able to go more in depth.