Aso is on the JR Hohi line, 1 hour and 40 minutes from Kumamoto by local train (�1080, change of trains may be required). There is also a limited express, the Kyushu Odan Express which makes four daily round trips with no change of trains required (65 minutes; �2180).
Kumamoto connects to Hakata in Fukuoka via the Relay Tsubame and Ariake limited express trains, and to Kagoshima via the Relay Tsubame and the Kyushu Shinkansen.
From Beppu you can get there in about 3 hours by bus (�2950) or 2 hours by train (�3740)
There are luggage lockers at Aso Station
