Shari-dake (1547m), south of town, is a spectacular volcanic cone and one of Japan's 100 Famous Mountains. Allow seven to eight hours for the return hike, which involves plenty of stream crossings plus spots with ropes and chains to help you. The views from the top are superb. Go between June and October, take supplies and use a bear bell.
Either use your own wheels to get to the trailhead (parking ¥500) at the Seigaku-sō (清岳荘) hut at 680m, or hop off the train at JR Kiyosato (清里町) station and take a taxi to the trailhead (¥4000, 30 minutes). If you get stuck, you can stay at the Kiyodake-sō for ¥1000 between June and September, but there are no meals.