One of Japan's 100 Famous Mountains, Rausu-dake (1660m) makes a great day hike, best tackled from the trailhead at Iwaobetsu Onsen (岩尾別温泉; 340m). Allow seven to nine hours for the 7km return trip. From the top there are stunning views of one of the Northern Territories Southern Kuril Islands (Disputed Territories).
The trailhead is 4km from the closest bus stop at Iwaobetsu, so without your own wheels you'll have to walk (a taxi from Utoro Onsen costs ¥3000 to ¥4000). The trail officially opens 1 July (though there may still be snow then) and closes when snow begins to fall mid-November. There's a route from Rausu as well, but it's more challenging.