21 Days Itinerary - May

Hello everyone, I'm finally able to answer after reading all your suggestions and doing a bit of research.
I'll try to clarify what we'd like to have experience in a Ryokan:

- Classical Building, not an hotel, may be reconstructed but at least has a wood structure with few rooms, not thousands.

- Day experience, at least the fundamental elements I've read here: https://www.ryokan.or.jp/past/english/receiving/index.html
Classic room, onsen, yukata, dinner, futon. Massage non required

-Decent Onsen, outside and inside. I can't really recognize the water quality, never done one, I blindly trust you on this.

- Nice Kaiseki dinner

I've seen many places online and I better point out what we'd like to avoid: hostels, aka fake Ryokans and Luxory Hotels with michelin dinner and comfortable beds (seen many of them near mt. Fuji).
I don't know if 200€ per person (25000 yen) is enogh, but looking at booking.com seems like you can get a nice room with this budget. We still accept suggestions over the budget.

Seems like Okuhide region is the best place for our itinerary.
Thank you everyone as always

I would definitely keep an eye out then for Okuhida and I think I saw some places in Asama onsen and the Utsukushigahara Highlands that might work. I think Okuhida might give you better rotemboro (outside onsen) but Asama and environs seem to have more older and classic looking buildings.

Outside of Booking, I would spend some time with Google Maps and just click on different accommodations that come up in the area you want to stay. It is a good way to find places that might not be on a lot of English websites.

I like Booking, I like that they (at least for Japan) always include all taxes in the price so there are no surprises. But there are also plenty of good places just not listed there. I would also read reviews with a grain of salt. People sometimes complain about really weird things (like the room being smaller than expected... well, Booking tells you the size of the room! or not liking the food, some people are picky eaters and I say this as a picky eater. So always read to see what the complaints actually are.)

Good luck!

That list is a good one, but you might struggle getting a place within budget that ticks every box. Consider going without the rotenburo in the ryokan and then picking that up in another place, eg Hotel Associa at Takayama (fantastic value hotel), Onsen Resort Hotel at Kamikochi.

I've stayed at places which had all of that, eg Arai Ryokan at Shuzenji and they are fantastic, but usually a lot of coin for the pleasure

Thank you once again @Rkold and @Lazy Pious,
I was checking out Arai Ryokan, not on our path, just to understand pricing. Seems like it's 837€ (107.971 yen) on booking.com, deluxe room for 4 people, still in our budget. Am I missing out something like extra expenses not listed?
If that is the price for a cool place than it sounds like we can afford it, not specifically Arai because has a different location.
Anyway, enjoying rotenburo in another location could be a nice move, we'll consider that too.
I can't thank you enough guys, much appreciated.

I'm sure I'll be back in a year or so with more questions :), since it looks like we won't be able to visit in May

Yeah, JPY80000 a night will get you something pretty magic. I've stayed in places that are under JPY40000 a night for two and they've been brilliant as well and to some extent I prefer them because they are more casual, but you wont forget a place like Arai ryokan in a hurry.