On the edge of town the beautiful Lake Ashi forms the focal point of the area, and the Hakone-jinja shrine rising from the water perfectly frames Mount Fuji in the distance - ideal for a photoshoot. If you're travelling during summer when the trails are open, and feeling fit enough for the 10-hour round trip (which usually involves some time sleeping in a small mountain hut) then you can dedicate a day to hiking to the summit for the reward of even more stunning views.
While in Hakone you'll also want to enjoy a boat cruise on the lake and visit the Hakone checkpoint, which highlights the region's important historical role. There are many excellent museums here too, so you might then like to step off the classic circular loop to visit some of these. The other major attraction in Hakone is the natural onsen hot-spring baths, so do as the Japanese do, and spend some (or all!) of a day soaking in their famous waters.