Is the 7 day pass recommended for this itinerary

Hi there,

Yes the 7-Day JR Pass will be a very good option for you, especially with the day trips you make to Hiroshima and Nara!
With the trip to Hiroshima alone you will be saving over 20,000 Yen. The only way you possibly could make better use of it is if you went the first day directly to Kyoto, this way to fare from the Airport would also be covered (about 3000 yen otherwise by Narita express).

To give you an about of the savings you can make, here is a little list:
Tokyo --> Kyoto ¥ 13,220
Kyoto --> Nara ¥ 690
Nara --> Kyoto ¥ 690
Kyoto --> Hiroshima ¥ 10,790
Hiroshima Miyajima ¥ 940
Hiroshima --> Kyoto ¥ 10,790
Kyoto --> Tokyo ¥ 13,220

For a total of ¥ 50,340 the 7-Day JR-Pass so you would be able to save ¥ 22,040 at least. Not bad at all!

You could even consider a 14-day JR-Pass, since you are traveling so much The price of that is 45,100Yen (or ¥ 16,800 difference with the 7 day JR-Pass). For instance if you used the 14-day JR-Pass to travel to and from Narita Airport and made a day trip to Nikko you would be at the same amount of savings as above.

Narita airport --> Tokyo ¥ 2,940
Tokyo --> Narita airport ¥ 2,940
Tokyo Nikko return by JR ¥ 10,860.

Additionally you could use the JR-Pass for local JR-trains in Tokyo.

If you decide to go for the 7 Day JRPass, you may find the [N'EX] + Suica card package useful.
Either way you will be able to make great use of your pass.

Hope this helps,
Daniel