Just after some confirmation that what I'm talking about here is all eligible under a JRPass and there are no obvious issues.
Day 1 - Saturday - Arrive (Narita). Catch bus
Day 2 - Sunday - Activate JR Pass. Travel around Tokyo using JR and Pasmo card.
Day 3 - Monday - Tokyo to Hakone (Romance car) + Hakone Free Pass
Shinagawa Station to Shinjuku Station (Yamanote Line - 20 minutes))
Odakyu Railway - Shinjuku to Hakone-Yumoto (Romance Car).
Hakone-Yumoto to Gora (Tozan Railway - 40 minutes).
Gora to Souun-Zan (Hakone Tozan Cablecar - 10 minutes)
Day 4 - Tuesday - Hakone to Kyoto - Hakone Free Pass / JR Pass
Sounzan to Togendai (Hakone Ropeway - 30 minutes)
Togendai to Hakone-Machi (Hakone Sightseeing Boat - 30 minutes)
Hakone-Machi to Moto-Hakone (Walking - 30 minutes)
Moto-Hakone to (Hakone Tozan Bus - H or K(pref) - 35 minutes)
Hakone-Yumoto to Odawara (Tozan Railway - 15 minutes)
Odawara Station to Kyoto (Odakyu Shinkansen - 2 hours 15 minutes)
Day 5 - Wednesday - Kyoto
Day 6 - Thursday - Day trip to Nara (use JR Pass)
Day 7 - Friday - Kyoto. Trip to Arashiyama (Sanin Line - use JR Pass)
Day 8 - Kyoto - Tokyo - Narita
I hope there's no crazy errors. We should get some good value out of our JR pass with this itinerary I think.