Help with Chubu Region/Tokyo/Kyoto Itinerary

Hello everyone! My boyfriend and I have been slowly planning an itinerary for our first trip to Japan this May, and we've hit a roadblock. We're going from May 11th to May 28th, but even though it's a decent amount of time, there is perhaps too much that we want to do.

We want to arrive in Tokyo and spend 4 or 5 nights there, we're thinking of taking day trips to Kamakura and Hakone, and maybe staying in Nikko for the night (we initially planned it as a day trip but it seems if you want to do the hikes it may be better to stay there). 

After Tokyo, we want to visit Central Japan (Chubu Region), more precisely Kiso Valley (Nakasendo trail, Magome-juku and Tsumago-juku), Shirakawago, Takayama, Okuhida, Korube Gorge and Yamanouchi. Here is where we are the most confused, should we pick a couple of base cities and take day trips from there? We do not drive and it seems it might be annoying changing hotels every night. On the other hand we don't know in which order to plan this bit of the itinerary, what places to pick as base,what is the best order in relation to trains and public transport, etc. Honestly, we are quite overwhelmed. 
For the last 4 or 5 nights of the trip, we want to stay in either Osaka or Kyoto and take day trips from there to: Nara, Himeji, Koyasan and Osaka/Kyoto depending on our base city. 

If there is any help you guys could provide, mostly in regards to the middle part of the trip, or if you think there is something not worth visiting, or something that may be missing from our plan, please let us know.

As you may guess from this post, we want to experience mainly 2 things, the main attractions that you CAN'T miss on a first japan trip and then nature, hiking, historic shrines and places. 

Thanks again, any help is incredibly welcome!

Japan Guide has an itinerary idea for Central Japan -
https://www.japan-guide.com/e/e2400_chubu.html

Note the number of days required to do all of that. You could go from Kanazawa to Kyoto (day 7 in the above) and skip the rest. Enjoy planning!

I think you are trying to achieve too much in not enough time. Here a proposed itinerary with less places, but a bit more doable, in my eyes.

11/May Arrival day in Tokyo. probably not a lot else going to happen on that day
12/May Tokyo
13/May Tokyo
14/May day trip Kamakura, night Tokyo
15/May overnight trip to Hakone, night Hakone --> ship luggage to Takayama and just bring a small bag for the two of you for the next days. (or even ship from Tokyo to Takayama)
16/May Magome (will be quite a lot of transport, night Magome or Tsumago
17/May Magome/Tsumago (most of this day will be transport and time in Magome/Tsumago), night Takayama
18/May Takayama
19/May Day trip to Shirakawa-go (or Ainokura or other Gassho village), night Takayama
20/May Day trip to Okuhida, night Takayama --> ship luggage to Kyoto and bring small back for Koyasan
21/May Koyasan (most of this day will be transport), night Koyasan
22/May Koyasan, night Kyoto --> or if your flight out of KIX is late in the day, you could do the last 2 days of your trip in Koyasan (1 night) and then go directly from Koya-san to KIX to catch your return flight.
23/May day trip Himeiji, night Kyoto
24/May Day trip Nara, night Kyoto
25/May Kyoto
26/May Kyoto
27/May Kyoto
28 Flight back from Kansai airport to home

- This removes Nikko (go to Shibamata in Tokyo instead) to see a similarly well decorated temple
- Removes Kurobe gorge (maybe plan some hiking in Okuhida)?
- Removes Yamanouchi (what exactly do you want to do there? See monkeys in the onsen? (That is frankly more spectacular in the winter. If you just want to see monkeys, either go to Arashiyama monkey zoo (I was never there, and not sure if I would recommend it), or go to Minoh park in Osaka (to the waterfall), normally there are some rowdy monkeys hanging around trying to snatch your ice cream cone. (although I was there a few weeks ago, and not a single monkey in sight).
- obviously the day trips can be moved around
- The Tokyo and Kyoto days in the above, to me seem to be the bare minimum

Alternative:

11/May Arrival day in Tokyo. probably not a lot else going to happen on that day
12/May Tokyo
13/May Tokyo
14/May day trip Kamakura, night Tokyo --> ship your luggage to Takayama and just bring a small luggage for the 2 of you for the next few days.
15/May overnight trip to Nikko, night Nikko
16/May Nikko - Shin Kurobe (although you will come through a place relatively close to Yamanouchi, I would give more time in the morning to Nikko and take a late train from Nikko to ShinKurobe (will take about 5 h), night around Shin Kurobe or Unazuki onsen
17/May Kurobe gorge, night in Takayama (but will again be a long day on transport)
18/May Takayama
19/May Day trip to Shirakawa-go (or Ainokura or other Gassho village), night Takayama
20/May Day trip to Okuhida, night Takayama --> ship your luggage to Kyoto and just bring a small luggage for the 2 of you for Koya-san
21/May Koyasan (most of this day will be transport), night Koyasan
22/May Koyasan, night Kyoto--> or if your flight out of KIX is late in the day, you could do the last 2 days of your trip in Koyasan (1 night) and then go directly from Koya-san to KIX to catch your return flight.
23/May day trip Himeiji, night Kyoto
24/May Day trip Nara, night Kyoto
25/May Kyoto
26/May Kyoto
27/May Kyoto
28 Flight back from Kansai airport to home

This removes Hakone (there isnt really a good alternative location to suggest for Hakone lovers) and Tsumago/Magome.
- You could do the Yamanobe no michi in Nara prefecture instead if you want to walk between old towns in the countryside