Be sure to pick up a Hakone Free Pass if you are planning to use public transportation on a visit to the area. It provides a discounted rate for unlimited, one-day travel on seven different types of transportation, including buses, a train, a cable car and ropeway, and even the sightseeing cruise on the pirate ship in Lake Ashi. Rates vary depending upon where you purchase the ticket, with cheapest rates in the Hakone area itself.
An excellent value is to get the Hakone Free Pass at the JR Shinjuku Station. Take the Odakyu Romancecar to Hakone-Yumoto Station; it runs direct and takes about 1 hour 25 minutes. This package costs 5000 for adults or 1500 for children. As well as the Hakone Free Pass, there are other discount packages for combinations of travel, such as a sightseeing boat and ropeway tour. For more information about the options: http://www.hakonenavi.jp/english/freepass/index.html