Hi Sharon,
Given your travel plans, here are two recommended JR Pass options:
The closest JR station to the Hakone area is Odawara Station. Please remember that the JR Pass covers travel only up to this station, and not the transportation within Hakone itself.
1) 14-day JR Pass (From Tokyo Station)
This would be a convenient option as it covers your entire long-distance itinerary (except for the travel within Hakone). You could activate it when you begin your travel from Tokyo, and it would cover all your journeys for the next 14 consecutive days.
2) 7-day JR Pass (From Odawara Station)
You would purchase a separate ticket for the initial leg of your journey from Tokyo to Odawara. You could then activate your 7-day pass from Odawara Station to cover all of your most concentrated long-distance journeys.
I hope this helps you plan an amazing trip!
Kind Regards,
Mariko