Just been on a similar loop. I would either base in Osaka and day trip to Kyoto or vice versa. Probably Osaka is best as you will want to be there late at night (when it comes alive) and for the early start at Universal.
Or, if money is no object, book for the duration in Osaka, l eave most of your stuff there and just go to Kyoto with a small overnight bag for one night. A lot of the temples are best seen early in the morning so that might work quite well.
I recommend a day trip to both Nara and Hiroshima. (you can do Hiroshima and Miyajima in one day, especially if you book the ferry that goes direct). https://www.aqua-net-h.co.jp/en/heritage/
An excellent day trip from Tokyo is to the Great Buddha at Kamakura and then Enoshima Island (temple, caves you see with candles, great food) and beach. If you are lucky, you will see Mt Fuji from the beach.
Kamakura: www.japan.travel/en/spot/1588/
Enoshima: https://www.japan-guide.com/e/e3117.html
Look at the local tourist board websites before you go to find local festivals and events. We were the only foreigners at an Obon festival at a local temple in Kyoto which was one of our more memorable nights. This is where the Kyoto events are: https://kyoto.travel/en/news/events_in_kyoto.html
We also had a great (and relatively inexpensive) tea ceremony experience at a cultural centre in Nara. https://www.sarusawa.nara.jp/services/
The baseball was fun! We were in amongst the super-fans which was brilliant. If you go to the Tokyo Dome, it is really near the Bunkyo Civic Centre (basically the town hall of the Bunkyo ward). It is free to enter their observation deck and you can see Mt Fuji on a good day.
Note, everywhere was a lot of walking and lots of stairs. I only took one pair of trainers and, in summer, that was a mistake. It was so hot that it would have been good to have two pairs and be able to alternate and allow one pair to dry out.
There are so many different train lines that I recommend researching all your possible routes before you go. It takes ages but is well worth it. I didn't use everything I researched but it was good to have all the possibilities mapped out and in some cases (Kamakura, Kyoto) there ended up being particular transport that was recommended for being historic or cute.