Hiroshima - go to the museum at the peace park. Also have okonomiyaki (which is very different from okonomiyaki in Tokyo/Osaka) ... best place we found for it there was Okonomimura - I think we ate in Yamachan on the 2F. Miyajima is a nice side trip from Hiroshima.
Osaka - mmmmm takoyaki. Osaka/Kyoto possible side trip to Nara.
Kyoto - you can get good curry udon here too
Tokyo - day trip out to Kamakura/Enoshima. Science and Nature museum at Ueno. Possibly a day trip out to Nikko.
Be prepared to have odd conversations with people who just want to practice their english on you (in my case last time it was a station cleaner at Hiroshima).
Hyperdia is your friend ... print off what trains you are aiming to get before hand and it makes making reservations a lot easier when you get the person at the desk who doesn't speak good english.
Great advice, is it mandatory to reserve seats for train travel?