When you say "to visit Mt. Fuji" exactly what do you mean?
Also when, since official season for going to Mt. Fuji is July-August.
As for Hakone, using your JR Pass, you can go as far as Odawara Station. After which you would have to transfer (eg pay) your way using Odakyu Trains or buses into the Hakone region. Depending on how far and how much traveling in the Hakone region you do, you might want to consider a Hakone Free Pass from Odawara:
http://www.odakyu.jp/english/freepass/hakone_01.html