If you head to Hiroshima, go to the museum but I wouldn't stay in the city, but continue on down the coast for another 15 minutes and take the short ferry crossing to Miyajima. Stay on the island overnight. Gorgeous.
Tokyo: I'd suggest you get to the Tsukiji fish markets at 4am - they are moving to new premises shortly so this'll be the last chance.
There is also this amazing 86 year old sushi chef: which has to be one of the great gastronomic experiences on the planet! - BOOK NOW!
Onsen: seriously, take a train down to the Izu peninsula. We have stayed several times overnight in a fantastic Onsen called Unryu: http://www.hotelunryu-izu.jp/onsen/
Food, tatami, Onsen - heaven. The real deal. Just be prepared to get your togs off in public.
Also not far out of Tokyo, about 90 minutes by train south of Yokahama, is the old temple area of Kamakra: http://www.jnto.go.jp/eng/location/routes/g_route/golden_tokyo_02.html
If you can't get to Kyoto, this is the next best thing.
Japan is full of amazing experiences ... enjoy! almost 5 years ago