Kyushu Itinerary Suggestions May 9-May 21

We will be visiting Kyushu for our first time. We will be coming from Osaka, Kyoto and Tokyo, so mostly we want to spend our time in the countryside. We will not be visiting Nagasaki and only 1 night in Fukuoka. Here's what we have so far
May 9 - Fly to Kagoshima (1 night)
May 10-12 Ferry to Yakushima (2 nights) and back to Kagoshima
May 13 Train to Kumamoto, stay 1 night, rent car
May 14-16 drive to Takochiho (2 nights)
May 16-18 drive to Kurokawa Onsen (2 nights)?
May 18-20 drive to Beppu (2 nights) ?
May 20-drive to Fukuoka (1 night)
May 21 - Fly home

My questions--Do we need 2 nights in Beppu? Should we stay in Kurokawa and skip Beppu? Maybe drive to Kitakyushu? Any help is appreciated. We don't care for 1 night stays, unless its a city. Thank you
SuzandJosh