Itinerary August (two 50's+23-yr+13-yr)

First time traveling to Japan. Please give input on itinerary below. Lodging has been secured for 5 nights Tokyo, 5 nights Kyoto, 1 night Tokyo
Day 1: arrive Haneda in afternoon, explore Tokyo
Day 2: explore Tokyo
Day 3: day trip to Asakusa & Odeiba; Giants game at Tokyo Dome in evening (tickets have been secured)
Day 4: day trip to Nikko
Day 5: day trip to Hakone
(Should we change something and add Kawagoe? Should we drop a day trip for additional time in Tokyo?)
Day 6: train to Kyoto, explore Kyoto
Day 7: explore Kyoto
Day 8: day trip to Nara
Day 9: day trip to Osaka
Day 10: day trip to Hiroshima & Himeji Castle
(Should we change something, drop a day trip for additional time in Kyoto?)
Day 11: day trip to Miyajima, train to Tokyo in evening (or drop Miyajima for something else or head back for day in Tokyo?)
Day 12: depart for Haneda

Day-11 will be very tough, unless you stay in Hiroshima the night before.

Day 10: start with a visit to Himeji in the morning,travel ontoHiroshima, then stay the night in Hiroshima.
Whether you want to drop a city for another day in Kyoto or Tokyo is a matter of preference, but day 11 is just too many hours on trains.

Day 10: start with a visit to Himeji in the morning,travel ontoHiroshima, then stay the night in Hiroshima.
Whether you want to drop a city for another day in Kyoto or Tokyo is a matter of preference, but day 11 is just too many hours on trains.

It is possible to visit Miyajima and Hiroshima as a day trip if you start early and only focusing on a few hours on the island and the Peace Park and Museum only. If you have others you want to see then you will need more time.

Hope this helps!

Do Hiroshima and Miyajima as a daytrip together on one day, and half a day in Himeji on another day.
I would probably combine Nara and Osaka, or Himeji and Osaka for one day in order to spend more time in Kyoto.