16 Nights From Tokyo to Hiroshima and Back

My travel buddy and I are trying to determine the best route to take through/around Japan to minimize time spent traveling between hotels/regions, as well as space out longer trips so we aren't going from a 6 hour train ride to 10 hour flight, back to back (for example). We've determined that it isn't worth spending just one night in any city (because of travel time, hotel check ins, etc.), so we are aiming to spend at least 2 nights in each area, guaranteeing us at least one full day of adventure before having to pack up and go to the next spot.

I think we've mapped out a basic plan, but we aren't sure about the timing between destinations or the very best way to get there along the JR route. Nothing is set in stone yet, so we'd appreciate some feedback :)

Day 1: Arrive at Haneda Airport - Train to Tokyo - Stay in Tokyo

Day 2 & 3: Tokyo - Stay in Tokyo

Day 4: Train to Hakone (Stay in Hakone)

Day 5: Hakone - Stay in Hakone

Day 6: Train to Kanazawa - Stay in Kanazawa (Best route from Hakone to Kanazawa??)

Day 7: Kanazawa - Stay in Kanazawa

Day 8: Train to Hiroshima - Stay in Hiroshima

Day 9: Hiroshima - Stay in Hiroshima

Day 10: Miyajima - Stay in Hiroshima

Day 11: Train to Kyoto - Stay in Kyoto

Day 12 - 14: Kyoto, Nara and Osaka - Stay in Kyoto

Day 15: Train to Tokyo - Stay in Tokyo

Day 16: Tokyo - Depart from Haneda

We'd like to work in some time for Takayama and/or Yudanaka when we are nearby, but aren't sure how to fit those in. Also, we'd like to take in a baseball game, Sumo tournament and Bunraku, if you have any suggestions. We will be arriving very early May 11th and departing very late on May 26 of this year.

Any information on how how best to expedite the in-country travel would be really helpful. We want to see as much as we can of this beautiful country while we are there!

Arigato!