A rail pass for this itinerary?

Hello!
Can you review this itinerary and see if a pass makes sense?

1) Tokyo - Tuesday March 27 to Friday March 30

2) Takayama - Friday March 30 - April 3 (leave April 3)

(Travel to Hida Region – Okuhida Osen go) (by bus from Takayama)

3) Kyoto April 3-7 – 4 nights

4) Koyo-san April -7-8 (1 night)

– Buddhist monasteries

5) Hakone - April 8-10 (2 nights)

6) Tokyo -10-13 (2 nights)

April 13

Fly out