Not sure if it makes the most sense to buy the 7 day pass and pay for trips outside that week or just puchase the 14 day pass? Also, would like to know when JR Pass is not possible - I think I have that figured out but confirmation would be helpful.
Itinerary:
Day 1: NRT -> Tokyo
Day 2 - 4: Tokyo
Day 5: Tokyo -> Matsumoto & Matsumoto -> Takayama (Nohi Bus)
Day 6: Takayama
Day 7: Takayama -> Hiroshima
Day 8: Hiroshima -> Miyajima
Day 9: Miyajima -> Mt Koya-san (partial JR? require Nankai pass?)
Day 10: Mt. Koya-san -> Kyoto (Nankai pass?)
Day 11: Kyoto <-> Nara return
Day 12-13: Kyoto
Day 14: Kyoto -> Tokyo
Day 15: Tokyo
Day 16: Tokyo -> NRT