fare from Fukuoka to Hiroshima

I am buying a pass but I don't know what the better day to activate it. Either going from Fukuoka to Hiroshima or buy a ticket for that day or activate it right away and buy a ticket for Tokyo to Narita airport?

Hmm. I'm not 100% I understand your questions, but I'll do my best!

The costs of the trips you mention:

1. Fukuoka/Hakata > Hiroshima = ¥8700
2. Tokyo > Narita Airport = ¥2940

Probably if I had to choose based on price alone, I recommend you choose to pay for the Tokyo > Narita leg, and use the rail pass to go from Fukuoka to Hiroshima.

Hope this helps!

To save money, use the pass on the most expensive days of travel - usually that is taking the bullet train.

There is good info seeing Fukuoka on:

http://www.thejapanfaq.com/fukpic.html

https://www.youtube.com/playlist?list=PL7LcPcmoSg-j4RLa6iC7ayvBAbOn8-028

For Tokyo, see:

http://www.gotokyo.org/en/index.html

http://www.jnto.go.jp/eng/location/regional/tokyo/index.html

http://www.ar.jal.com/world/en/guidetojapan/city_information/tyo/see/akasaka/

http://www.japan-guide.com/e/e2164.html