Longtime reader, first-time commenter - thanks for all the online musings you've shared!
This is not particularly off the beaten path, but if the thought of going to Hiroshima appeals to you, definitely go. It's less than a 2 hour bullet train ride each way from Kyoto. The museum dedicated to the atomic bomb is very well done, and I found it incredibly moving and meaningful to spend time with the enormity of that human decision and historical event. The better part of a day was enough, leaving time to go further down to Miyajima and check out the floating torii gate and friendly deer (bonus tip: check that the latter isn't under construction; when I went it was being worked on and all I could see was a billboard of the gate atop the scaffolding it 😂).
I’m in Hakone right now, after visiting Tokyo/Kyoto/Hiroshima (which is pretty much what everyone else has recommended, and I agree wholeheartedly). One tip for Kyoto - I found the temples to be unbearable with heat and hordes of tourists anytime between roughly 10:30am and 4pm. It’s worth trying to visit the popular ones on either end of the day as much as possible. Also, the Okochi Sanso Garden in arashiyama (east Kyoto) was the most serene place of the whole trip for me.
The adventure playground called Hanegi Playpark – nicknamed the ‘Savage Park’ – (see Amy Fusselman's book of that title) and this 12 floor stationery store https://www.timeout.com/tokyo/shopping/g-itoya. Both are big some day I'll get there dreams for me.
You'll almost certainly be going to Kiyomizu-dera in Kyoto (a tourist staple but more than worth it). Try if possible to do so at sunset. It's one of the finest views in a country packed with them.
If you climb Fushimi-Inari-Taisha (the mountain with the thousands of torii gates) at the top there's a sort of area behind the main shrine that offers a calm moment of pleasant openness.
If you're interested in whisky, Zoetrope in Shinjuku has all (or very nearly all) of the whiskies made in Japan, and the owner is knowledgeable and great at recommendations.
You absolutely must check out onsen (community baths, usually attached to hot springs or a mineral water source) while in Japan.
It is a very Japanese, but absolutely wonderful cultural experience and they're everywhere in Japan. Link seems to be down now, but this is a very good resource to understand more about onsen culture: https://one-from-nippon.ghost.io/r/b1e136fc?m=26916005-7fc6-4acf-8017-2b9af022fe18
Additionally, I highly recommend just wandering into tiny ramen and sushi joints, especially outside of the tourist cities, especially in Kyoto. It's a little awkward, but you end up getting into some fascinating conversations.
Also, get a JR rail pass and really use it! Japan is an amazing country and there's so much to see!
Spend a night or two on Koyasan (and walk the cemetery at night)
I wouldn't say it's a must do but I enjoyed hanging out in Hakone, was super peaceful there (wrote about it too: https://edwardsays.substack.com/p/ode-to-the-tranquil). Prob not worth going out of your way for. Looking forward to getting perfume'd up 👍🏻
I was secretly hoping it'd be called "All the Wrong Scents"