Been twice, so no expert, but have some experience.
First off: language. Although many may be intimidated/embarassed to try to speak/converse with you (except for hotel staff), most of the younger generation have all learned english. So a BIG tip I learned was that if you ever get stuck communicating - simply WRITE IT OUT. They all learn to read and write. And this worked perfectly for me.
Hiroshima: you HAVE to visit (and take your time) the a-bomb museum and park. I’m sure it is on your itinerary, but it is a definite must. Not too depressing, and very educational.
If you have the time, take the ferry over to Miyajima. It was a pretty cool place to walk around. But beware the begging/annoying wild deer. They are so used to people feeding them (you can buy little bags of veggies to feed them all over the place), they can be downright annoying to get food (poking their noses in your pockets, etc.)
Tokyo: you probably have a full list of temples and what not of tourist attractions to see. If you have Tokyo Tower on the list, I would pass. Yes, you can get some nice views of the city, but it’s pretty commercial (a zillion little gift kiosks await you once you take the elevator down).
There is both the subway and light rail systems to get around. I was a bit more intimidated with the subway. But the light rail is pretty straightforward to use. It may seem a bit overwhelming, but it is not that bad. I would encourage you to explore some areas on your own: Roppongi, Shinjuku, etc… But as you walk around, take note of landmarks. It is easy to get disoriented and confused in some of the areas.
Kyoto: Definitely check out the palace/castle. This will take you right back in time to the shogun days (or “The Last Samurai” if you’ve seen that flick).
Last but not least, I would highly recommend doing the on-sen (public bath) at least once. Yes it is intimidating, and may not be something you’re used to. But especially if you’re all sweaty and grimy from a day of sightseeing, a great way to relax.
The procedure is pretty simple:
There is usually a changing room, where you can toss your clothes and change into a towel.
You don’t just jump right into the baths - you clean yourself first. There will be a row of “sit down shower” stations - little stools with shower heads (removable, usually) and soap. So you take a station, and wash yourself thoroughly.
Then you can go hang in the bath. And you pretty much just sit there and maybe dip into the water. No bathing. No swimming laps 
When you’re done, you may want to shower again at one of the stations.
I was too intimidated on my first visit, but on my second visit I tried it and loved it. It’s really relaxing and you feel really refreshed when you come out. I’d recommend it before going out to eat. A nice way to get rejuvenated before heading out for the evening.
That’s all I can think of for now. More if I think of stuff.