In/near the Hakone area, I believe the closest bullet train station (albeit the "local" bullet train called Kodama) is at Odawara. From Odawara, take a Kodama shinkansen to a station from where you can get a regular express shinkansen (called Hikari). You could either backtrack to Shin Yokohama, where many Hikari stop, or go down to Nagoya perhaps. Hikari's are included in the rail pass fee. IMHO, the fastest shinkansens, called Nozomi, which are not included in the JR passare not worth the extra charge. JNTO have a nice little timetable for almost all JR trains and most of the main private trains.
I agree with Sweet Willie's suggestion of the peace memorial and Miyajima Island.
[This message has been edited by unagi1 (edited 06-03-2001).]