Best traditional ryokan Osaka to Tokyo

Hi, we are a family of 4 (kids 7 and 12). We are wanting a traditional ryokan in or between Osaka and Tokyo with tatami mats and futons with great architecture and onsen (garden would be a bonus) in September. Looking at a max price of $1000 for the night.

I have fond memories of Ochiairo in Izu peninsula. It was pretty expensive but probably 1000 USD for one night should be within budget (have never spent that much on a hotel myself. I vaguely remember I spent for 2 about 400 Euros there. But that was before Yen depreciation and before covid inflation.
https://www.ochiairo.co.jp/en/facility/

Alternatively I could recommend Dorogawa onsen.
I don’t remember exactly in which ryokan I stayed there. It didn’t have a rotenburo and was more simple than the one above. But the village is very nice. While Ochiairo isn’t in a specially nice village.
Dorogawa was name is reachable by public transport from Osaka. But if renting a car is an option it might be a good opportunity to discover some other places in the area (like Asuka, Muroji, Akame 48 falls, Kashihara Jingumae, Yoshino, Omiwa jinja…. There is sooooooo much to discover in inner Nara prefecture. My personal favorite place in Japan. Just spending here (around Sakurai) a few days myself. And so much more to discover.

The ryokan in Izu I think is reachable by taxi from Shuzenji station and maybe the ryokan (at those prices) has a pickup service? But again renting a car in Shuzenji would be a good idea. Many things to discover as well in Izu peninsula. Something the kids may enjoy is the capibara zoo. With capibaras chilling in an onsen.