Tokyo-Takayama-Nagano-Hiroshima-Osaka

Hi Diana,
Let's have a look at ticket prices and see if a JR Pass would be useful.
Narita Airport - Tokyo ¥ 2,820
Tokyo - Takayama ¥ 14,410
Takayama - Nagano ¥ 10,790
Nagano - Hiroshima ¥ 17,340
Hiroshima - Miyajima return ¥ 1,140
Hiroshima - Nara ¥ 11,370
Nara - Kyoto ¥ 710
Kyoto - Osaka ¥ 560
Osaka - Kansai Airport ¥ 1,190

For a total of ¥ 60,330 or ¥ 13,940 in savings as the 14 day JR Pass is ¥ 46,390.

As for staying in Osaka or Kyoto, I'd stay in Kyoto as it is a nice change for the metropolis life found in Osaka/Tokyo. Especially since you will visit Tokyo as well. Travel time between Osaka - Kyoto is less than 30 minutes, so it's easy to make trips between both places.

Hope this helps!
Daniel