Hi there!
Lets take a look at your trip costs to see if your journey costs could fit well into one of the Japan Rail Pass types (assuming you fly into Osaka Kansai Airport):
- Kansai airport > Osaka: ¥2400, (53mins, 57km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Nagoya: ¥5440, (49mins, 147km)
- Nagoya > Nakatsugawa: ¥2940, (48mins, 79km)
- Nakatsugawa > Magome: ¥2940, (48mins, 79km)
- Magome > Nakatsugawa: ¥2940, (48mins, 79km)
- Nakatsugawa > Matsumoto: ¥4180, (75mins, 108km)
- Matsumoto > Takayama: ¥11310, (304mins, 354km)
- Takayama > Osaka: ¥10310, (220mins, 357km)
- Osaka > Kansai airport: ¥2400, (54mins, 57km)
TOTAL: ¥43,000 for 10 legs
As a 14 day rail pass is ¥45,100, you would need to do a little more travel to make one worthwhile based on your itinerary. Including some very simple travel, such as a return to Hiroshima will mean you make great savings on the travel for your trip, as any further JR travel will effectively be free.
You can look up train timetables and costs for all of your legs at the Hyperdia travel planning website and learn how to use Hyperdia for Japan Rail Pass holders through our video blog.
Hope this helps!