The active volcano of Aso will bring quite a significant amount of tourists to the small town of Aso. Aso Tourist Information is located in it's own building just beside the Aso station.
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 (九州横断特急), 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 two cable car lines up to the mountain. Aso Nishi (west) cable car station is easily reached with a bus from the Aso station. The last bus back from Aso Nishi cable car station leaves at 5 pm. You can also hop on and off the bus at the bus stop near the Aso Youth Hostel. If you're driving, a toll road goes right up to the station and if you're prepared to pay, you can actually drive up to the summit of the crater.
Aso Higashi (east) cable car station can be reached by taking a local train to Miyaji station (2 stops from Aso station) and then walking up the road to the cable car station.
Aso Volcano Museum.
Aso Shrine. An old shrine dedicated to the gods of harvest and planting.
Aso Osaru-no Sato Saru-mawashi, 793 Shimono, ☎ +81 967 351341. This theater has man and a monkey stage shows.
Aso-san. The volcano is still active and sulphuric steam can be seen coming from the Mt. Nakadake crater. However, you should be aware, that the summit of the crater has been extensively geared for Japanese mass tourism - paved roads can take you right up to the crater and it can get quite crowded during the peak season. However, if you want to get away from the crowds, you don't have to walk too far.
WARNING: The mountain spews sulphurous gases from the crater of Mt. Nakadake. Sometimes, when the winds blow from the crater towards the crowds, the cable car lines are shut down, so you might not be able to reach the summit. They will start operating again, when the winds turn - sometimes you will only have to wait half an hour or so. If you want to check, before starting your hike, the owner of the youth hostel is able to tell whether everything's in operation.
If you have extra cash to spare or you want to have an aerial view of Mount Aso, you can take the helicopter ride, which is not far from the Mount Aso Museum. It cost ¥5000(adult)/¥4500(child) per person for a 4 mins ride but the view is astounishing!
Various hiking trails around Aso-san can provide you anything from a nice afternoon walk to a good days hiking. If you're interested, be sure to pickup a hiking map from the friendly Aso youth hostel.
There are also several hot spring resorts around Aso. Contact Aso tourist information office for more information.
Besides the usual tourist trinkets you can buy from the Aso Nishi cable car station, there's not much shopping to do around here. Your usual supermarket is a couple blocks south from the Aso station.
There are some restaurants and a noodle bar near the station. In Aso Heights, there is a delicious cheese cake. Japanese lunch box can be bought at Aso JR Station.
Aso Youth Hostel, 922-2 Bochu, ☎ +81 967 340804, . The youth hostel is quite ascetic, but is cheap and the owner is very helpful. No breakfast, but they sell stuff like instant noodles you can have in the morning. They also have a simple Aso hiking map revealing the different trails around the mountain. It's about 20 minutes walking uphill from Aso-station. (Dorm ¥2450)