When you go to Kagoshima, Kyushu Shinkansen is the best way to get there. It is fast and the trains come very frequently. But if you have a time, please consider the route from Kumamoto to Kagoshima-Chuo via Hitoyoshi and Yoshimatsu on Hisatsu line (肥薩線). It is very scenic route. JR Kyushu operate very attractive trains on this route.
Takachiho is known as the land of Japanese mythology. There are lots of shrines and places that are related to the mythology. And also Takachiho Gorge is one of the “Must-See” spots in southern Kyushu area.
I visited there in mid March, 2012. I would like to share my experience with you. I hope this will be helpful for your trip to Takachino.