Do I need other transportation rather than JRPass?

Hello everybody,

I'll be traveling to Japan next week, and I'm planning to do the following:

17-09-2014 Arriving in Narita
18-09-2014 Tokyo
19-09-2014 Tokyo
20-09-2014 Tokyo
21-09-2014 Tokyo (Day trip Kamakura)
22-09-2014 Kyoto
23-09-2014 Kyoto
24-09-2014 koyasan/kumano
25-09-2014 koyasan/kumano
26-09-2014 Kyoto
27-09-2014 Kyoto (Day trip hiroshima)
28-09-2014 Hakone
29-09-2014 Hakone
30-09-2014 Flight from Narita

I have a 14 days JR Pass. What do you think of this plan? Any suggestions?

Do you know in all theses place, where JRPass do not work?
Probably in the:
• Tokyo subway, • kyoto local transportation, • koyasan/kumano local transportation, • Hiroshima local transportation, • hakone transportation I’ll have to buy other kind of tickets, right?

Any idea if it’s easy to go from Koyasan to Nachi falls in Kumano?

Thanks for the help.