Should I get 7day or 14day JR PASS

Itinerary a follows:

SEPT 25th - OCT 11th 2015

Sept 26th - arrive at 3:30PM in Narita airport and travel to Tokyo Japan
Sept 27th - Tokyo - enjoy the Ikebukuro Fukuro Matsuri Festival
Sept 28th - Tokyo - shopping and finding KITKATS
Sept 29th - Minakami to do rafting and canyoning, stay in takaragawa hot springs
Sept 30th - Hacioji City to climb Mt. Takao leave to get back to Tokyo
Oct 1st - Tokyo - FREE admission day to parks and aquariums
Oct 2nd - Kyoto
Oct 3rd - Kyoto
Oct 4th - Kyoto day trip to NARA
Oct 5th - Kyoto day trip to OSAKA
Oct 6th - Kyoto day trip to OSAKA
Oct 7th - HIROSHIMA stay night in Miyajima
Oct 8th - day in Miyajima, leave in evening for TAKAYAMA
Oct 9th - TAKAYAMA enjoy the TAKAYAMA FESTIVAL
Oct 10th - Leave Takayama for Narita,be in Narita by 6PM and watch the famous fireworks show
Oct 11th - Leave Narita airport for home at 11AM

Do you think the 7 day or 14 day pass would be better? If 7day when should I enact it? Anything I am missing from itinerary that you would recommend? Any suggestions for how to see the Takayama festival?

Thanks to all for the help!! We are so excited to visit Japan!