Go to the top of this page and click on Hotels. Then, enter Kyoto as the city and your dates. In the list on the left (under "Style") you can filter by ryokan. Many choices with reviews. By the way, sleeping on the floor is normal at all ryokan.Edited: 16 May 2018, 21:28
Thanks. For the info. Will look up 👍🏻
It's more like laying futon mattresses over tatami mats to make a comfy bed (and not sleeping on the floor).
As my hometown is about 40 min from Kyoto, I rarely stay in Kyoto. I am generally skeptical about ryokans in Kyoto (for the best experience, I would recommend hot springs ryokan in historic onsen towns like Kusatsu Onsen and Kinosaki Onsen), but how about this newly rebuilt and moderately priced ryokan (not far from Nishi-Honganji and Kyoto Railway Museum): https://www.yunoyadosyouei.jp/ryokan-kyoto/