The Nakasendo trail is lovely. We did that in November 2018 and enjoyed it so much we are returning next November. This was the height of kōyō (fall color season) but it was not the least bit hectic or crowded. I have no idea what it would be like in July, but I doubt there would be more people than we saw.
https://www.japan-guide.com/ad/nakasendo/
How much time do you have? It needs 4-5 days to walk the popular section through Kiso Valley and Maggie area. We went with a small guided group, so I cannot help you with travel and lodging logistics. The US small-group tour companies do not offer this in summer, only in spring and autumn, but I see this Japanese company offers the Nakasendo in July and they have some availability:
https://walkjapan.com/tour/nakasendo-way-the-kiso-road
And of course there are companies that will help you set it up as a self-guided walk (hopefully with luggage transport for you).
If you don’t have that much time to spare for your “vacation”, you could consider visiting Naoshima, the so-called Art Island.
https://uno-hotel.com/en/
This could be a 2-night stop on your way south from Kyoto to Miyajima. You would leave the Shinkansen at Okayama and take a little train 45-55 minutes down to the port city of Uno, where you catch the ferry for the short ride to Naoshima Island. When we did this last November, we spent the first night in Uno at this nice modern hotel with a fantastic breakfast:
https://uno-hotel.com/en/
The next morning we caught the ferry over to Naoshima to spend the day and the night there. I booked the Benesse House hotel on the day reservations opened up (I think 6 months in advance). It was expensive, but well worth it.
https://benesse-artsite.jp/en/
The hotel shuttle met us at the ferry and carried us to the little town of Honmura, where we spent half the day exploring the Art House Project before meeting the little shuttle to take us to our hotel.
https://www.japan-guide.com/e/e5479.html
Our luggage was waiting for us in our room, and we had the rest of the afternoon to relax, stroll the beach, and admire the sculptures here, before a delicious French-inspired dinner in the hotel restaurant (included in the package).
We spent the next day exploring the Benesse area museums, including architect Tadeo Ando’s Chichu Art Museum, designed to display marvels like 5 large Monet paintings in totally natural light.
https://benesse-artsite.jp/en/art/chichu.html
This page has a fairly complete list of all the art museums and installations, some of which are on other islands:
https://benesse-artsite.jp/en/art/
Take particular note of the Bath House, which might be fun, if you enjoy this aspect of Japanese culture (I do, my husband does not):
https://benesse-artsite.jp/en/art/naoshimasento.html
https://japanjourneys.jp/kagawa/naoshima/attractions/i-love-yu-bathhouse-sento/
I think I have just talked myself into putting a return to Naoshima on our itinerary for next November.