Among your first stops should be Hakone Visitor Center. Here, you'll be able to find your bearings and get some great ideas before you set out exploring.
This tourist information center is in Sengokuhara, a place that has loads going for it! Gotemba Premium Outlets, Lake Ashi, and Hakone Kowakien Yunessun are other interesting sightseeing choices close by when you're done at Hakone Visitor Center.