We went for three weeks in September for a "once in a lifetime" trip
Hiroshima was a day-trip for us; outside of the memorial park and museum, there wasn't much else we wanted to see.
Osaka was another day trip for us but I wish we would have spent longer. Don-tombori is a must see, especially at night. We also squeezed in Osaka castle and the aquarium. In retrospect, the aquarium we could have skipped. It's considered the largest in the world but that's because the volume of the main tank in the middle spans all of the floors. I've enjoyed other aquariums more.
Kyoto was our "base of operations" and we took trains everywhere. Kyoto was preferable to Tokyo for us. I thought Toronto, Paris, London, LA were huge... it's nothing like Tokyo. We saw the usual touristy things in Tokyo and mainly went for Disneyland/Disneysea for our daughter. The Imperial Palace grounds are not opened for regular folk so there's not much to see there other than the immaculate condition of the parks and walkways.
Don't miss Asakusa district in Tokyo... another thing we rushed through and would have liked to spend more time exploring. We even thought having our hotel there would have been better (we were near Tokyo Bay). We went for a "sumo" dinner which was a great event:
https://asakusa-sumo.com/menu/
Take your time, enjoy everything, and be prepared to make mistakes taking the trains.