7 day or 14 day JR pass for this itinerary?

Hello! Our itinerary is:

Day 1: Fly into Osaka Kansai, train to Kyoto
Day 2: Kyoto
Day 3: Train to Hiroshima, stop off at Himeji Castle for lunch
Day 4: Hiroshima
Day 5: Miyajima Island
Day 6: Train to Tokyo
Day 7-14: Tokyo, with side trips to Kamakura and Mt Fuji

So, I was wondering it would be more economical to get a 7-day pass since most of the travel is in the first week, or to get a 14-day pass?

Thank you!

A 7-day pass will be slightly cheaper than regular train tickets in the first week, but a 14-day pass will not pay off.

You could also get a JR Kansai Hiroshima Area Pass, and then get a Platt Kodama ticket to Tokyo. You would not have reserved seats, and the trip to Tokyo would be on the slower Kodama Shinkansen. You would also probably want a Icoca and Haruka package for the fist day to get to Kyoto. Here are some links:

http://www.japan-guide.com/e/e2359_icoca_haruka.html
http://www.japan-guide.com/e/e2359_003.html
http://www.japan-guide.com/e/e2361_kansai_hiroshima.html
http://www.jrtours.co.jp/kodama/en/?scid=jtt_kepEng001

Icoca & Haruka Package: 3030 yen
JR Kansai Hiroshima pass: 13000 yen
Kyoto to Tokyo: 10300 yen

Icoca card only: 2000 yen
JR 7 day pass: 29110 yen

This is only slightly better value in terms of cost. You would also have to catch the Haruka Linited express to Kyoto. I would probably go with the extra amount for the 7 day pass, and go to Kamakura on the last day of the pass. If you were wanting to spend more time in Kyoto before going to Tokyo, it would be a lot better than a two week JR Pass.

Either way you go, you would probably use the Icoca card to get around Tokyo after you get there. On the second day of your trip, you will probably get around Kyoto on the bus system. Even if you plan to get the 7 day pass, if could actually be worth it to get the Icoca & Haruka package so that you don't activate the 7 day pass until day 3 of your trip.

I hope these links help.

I would spend longer in your first 7 days at each place rather than spending 7 days in Tokyo. Hiroshima is lovely and well worth more than a day trip.