My wife and I have dietary restrictions, so we typically look for hotels/apartments with a kitchen/kitchenette where we can make some meals.
For our most recent Kyoto trip we used booking.com with the filters for places with kitchen/kitchenette, and while the choices were limited, there were some. I also use Agoda for searching for places in Japan, though typically I book through other means.
For hiking and natural beauty:
I am currently planning a hiking trip in Shikoku. There are a lot of hiking options and Shikoku is considered much less touristed. There is also the Shimanami Kaido biking trail across the inland sea.
There is the Kumano Kodo pilgrimage trail in Wakayama. This can be done as a series of day hikes if you like. I did this in November and it was very quiet. Visiting the three major shrines, digging our own onsen into the banks of a river, enjoying the cave onsen in Hotel Urashima, eating fresh sashimi. Overall a great experience.
I have done sections of the Nakasendo Way in the Kiso Valley. Heading from Kyoto to Nagatsugawa, hiking the section from Nagiso to Magome (or the section ending in Narai), and spending a night or two in Matsumoto might be a nice slow trip back to Tokyo from Kyoto.
In my opinion Hokkaido (particularly Eastern and Central Hokkaido - Shiretoko National Park, Lake Akan, Daisetsuzan National Park) can't be beat for hiking and natural beauty in Japan. I was there in September (apparently a slower period). Quite a ways from Tokyo and Kyoto, but you may be able to swing it with domestic flights.