Mount Aso and Takachiho Gorge

Hello!
I'm planning to go to the Kyushi area by April or Mai. I would like to visit Mount Aso and Takachiho gorges (in different days), by bus or train, and I don't know what city would be the best place to begin: Kumamoto, Miyazaki or Beppu?
Thank you so much

I would assume that the direction you are originally coming from would be a big factor on determining the best starting point. But if that is not a factor, Kumamoto will be the best starting point. Mount Aso can easily reached from there:
http://www.japan-guide.com/e/e4551.html

Public transportation between Mount Aso and Takachiho is not quite as straight forward, though, as explained here:
http://www.japan-guide.com/e/e8051.html?aFROM=4552_8050