Hi Molly... We just got back from Hiroshima to Kyoto today. Hiroshima was heavy but worth the trip. Kyoto is a blast. Couple of suggestions for Kyoto, the Nishiki market is fantastic and well worth the time. Can't recommend it enough. Also the Golden temple and zen garden nearby is incredible.
If you are at all into cooking, we attended a cooking class that started in the Nishiki market done by Taro Saeki in Kyoto. He teaches a class on how to make a lot of the core Japanese cuisine and ends the day with you eating the meal you prepared. It was truly the highlight of our trip. Taro-san is an amazing host and we learned a ton from the class.
For the train travel do not worry, it's incredibly easy. Hiroshima has signs everywhere that direct you to the trolly to take you to the bomb site and museums, also there are really good eats around there as well. Kyoto, wow I would love to have a few weeks here, but alas we leave in the morning.
Scott