Traditional ryokan with onsen in Hakone?

Hi there!
I'll be fulfilling my childhood wish of going to Japan this upcoming november and I have really wanted to stay at a ryokan to get a bit more of a grounded experience. I'll be staying in osaka, Kyoto and Tokyo so I've been looking at onsen ryokans around the shinkansen line between the cities, mainly Hakone. As I've tried to browse places to book it's been hard for me to find a ryokan that fit me and my partners needs and wants.

We've been looking everywhere for a more traditional ryokan (futons and Japanese dinner/breakfast) with private onsen. My partner has tattoos so a place with only a communal bath wouldn't work unfortunately. We don't really care for the western styled rooms and menus since we really want to immerse ourselves in the country's culture.

My question is do you guys know or have been to any onsen in the hakone area (or along the shinkansen line between osaka and Tokyo) that you recommend? How much do you think the average cost per person would be otherwise with these criteria in mind?

Every little tip and recommendation is very much appreciated! Thank you guys so, so much in advance!

Have a look at Fukuzumiro Honkan at Tonosawa (a short walk from Hakone Yumoto). I have stayed in dozens of ryokan over the years, this one would be the closest I would say to stepping back in time, the place is like a museum. It has reserved baths (see the website) though in my experience if you go mid week there is usually barely anyone there and you could have the onsens to yourself.

Unfortunately only one room has a bathroom in it (the room is fantastic), the rest you have to go down the hall a bit to the toilet. But that comes with the territory, as the place is so old. We stayed in two rooms there, a normal one and then the one with bathroom and private bath, both were great but it is nice to have a toilet in the room for convenience.

Staff are fantastic, as is the food. I think they even do vegetarian from memory, if you want it. And the location is brilliant, you'd think you were 100 miles from town, but in reality it is probably 200m away. I could waffle on about it forever, it was really one of my favorite places.

Hi. I suggest you look at Hakone Airu on www.hakone-airu.com/en It isn't completely traditional but it has private open air baths attached to each room, ensuite facilities, traditional furnishings and Japanese meals. We had an excellent 2 night experience there and would recommend it.

Hi again, I just looked at prices for Fukuzumiro for mid-week in June, see it will depend on the room but it ranges from about AUD$600 to over $1,000, breakfast and dinner included. If you were paying for the dinner at a restaurant it would be $100 a head, and brekkie would be $40 a head, so essentially you've got about $250 plus in food cost there (this is how I rationalise it lol), so the accommodation itself is not as expensive as you first might think.

Usually for a decent ryokan in a popular area, I would expect $600 - $800 a night, full board. It is a lot cheaper in more rural areas, we stayed at Kiso-Fukushima last trip for a few nights at under $400 per night for a couple, full room and board in good rooms with nice views.