I quite liked Kyoto. The Nijo Castle in Kyoto is beautiful (and a very capable defensive castle in its time). The floor was made to intentionally creak so that no one could sneak up on the emperor to kill him (when there you can read about how well that worked out at one point). You can try to walk lightly and the floor will still make a sound (of course we all tried this). There are so many temples in Kyoto that I cannot imagine anyone visiting all of them unless you live there for a few years and make it your mission in life. It is definitely worth visiting at least some of them. My understanding is that Kyoto was largely spared during world war 2 which is a very good thing and leaves a lot of interesting things to see that are very old. I remember visiting a temple that was intentionally designed to survive earthquakes, and has survived at least many hundreds of years.
The bullet train from Tokyo to Osaka was an experience. It is so fast that anything close to the train goes by so quickly that at first you think that your eyes are defective. It however is very smooth (it probably has to be to move so fast). If I already wanted to move between these two cities I would take it again, but I would not go out of my way to take it.
I liked Hiroshima quite a bit. I was there for a week long business trip. With a day to go I was out of work to do and it was going to be too expensive to change my flights, so I wandered over to the peace museum. It is VERY well done and is very much worth a visit. I found it very moving. They probably could have made it anti-American but really didn’t. Instead they have a very thoughtful presentation of the issues that led up to the bombing. It is indeed sad however.
To me this seems like a sensible amount of time. It is such a distance that once there you want to take advantage of the time spent getting there and getting accustomed to the time zone. You could spend a lot longer and never run out of things to see, but after two weeks many of us (myself included) are ready to get home already.
One comment with respect to jet lag: On one trip to Japan I took a very early flight from Boston to Chicago, and then a very long flight from Chicago to Japan (I am not sure if this was to Tokyo or Osaka). I had to get up very early for the first flight. The result was that I was horribly tired. We took off from Chicago around noon, and I immediately fell asleep and slept for something like 10 hours, waking up as we were getting close to Japan. The result was that I was pretty much already on Japan time before we even arrived there. This was the least jet lag that I ever had on a trip to Asia. Getting on Japan time as soon as you can is valuable, although it is not always easy to do.
In general for trips to Asia I used to try to not plan to do much on the first day there. In the unusual case where jet lag did not hit me much, there is enough to do just wandering around. I always felt safe in Japan, although being a large man (mostly vertically) might help in this regard.
I always stayed at either the hotel that was hosting the conference I was going to, or at the hotel recommended by our local sales office. As such I have no idea what hotels to suggest.
You might want to ask your doctor about vaccinations. I did get some vaccinations for my trips to Asia (hepatitis A and B come to mind) but at least part of this might be more due to having many trips to many parts of Asia. Japan did seem clean to me in addition to seeming to be safe. I did run into some places, including some restaurants, where their English was rather limited.