Which day to start our JR Pass

Hello,

We are planning a 15 day trip to Japan for our first time Dec. 27th - Jan. 10th. I'm not sure what pass we will need. Here is our tentative itinerary. We are both in our mid 30's and very adventurous. Any suggestions on our itinerary or help on would be greatly appreciated!

Dec. 27 - Arrive into Narita, spend the night in Tokyo
Dec. 28 - Travel to Nagano
Dec. 29 - Nagano to Matsumoto Castle to Takayama
Dec. 30 - Takayama to Kyoto
Dec. 31 - Kyoto
Jan. 1 - Kyoto to Miyajima
Jan. 2 - Miyajima to Iwakuni
Jan. 3 - Iwakuni to Osaka
Jan. 4 - Osaka
Jan. 5 - Osaka (or day trip somewhere)
Jan. 6 - Osaka to Tokyo
Jan. 7 - Tokyo
Jan. 8 - Tokyo (possible day trip somewhere)
Jan. 9 - Tokyo (possible day trip somewhere)
Jan. 10 - Depart Haneda airport in the evening

Thanks!
Teresa