I want to stress, I have not stayed in them yet but.....
I was looking at the Gentle Fox near Fushimi Inari:
http://gentlefox.jp/English/
Yutaka Hotel near Nijo: so new it has no official website, but you can see it on Booking or via Google, just make sure you don't look at the steakhouse with the same name.
If your group is not so big, I heard from a family of 3 on Japan-Guide that the Hotel Anteroom is amazing. If you book far enough out they have some amazingly low rates.
All of these options are below $150 a night some with the right exchange rate are closer to $120, or at least they were for my June 2018 dates. I am personally trying the new Integrate in Kyoto probably (I am debating there are the Anteroom.) They offer free french roast coffee, free smoothies between 6-7 am, and free wine XD; The rooms don't look as nice as the Anteroom, but I like the location in the central shopping district. If I was a larger group I might pick one of the other places, but we're just two. I stayed in the Hana Touro last year (about $175) and loved it, but I am trying to be more careful with costs because I am splurging for 2 nights in Tokyo at my favorite hotel.
I want to stress, I think the Yutaka, Integrate, and Anteroom have all opened up since my trip to Kyoto June 2017. I don't think the Gentle Fox was open in June 2017 either, I know the Hana Touro was newly opened when we stayed there in June 2017. If you're looking to go to Japan 6 months from now, I would keep looking, there is a huge hotel boom going on right now and who knows what new and interesting places will open.
Someone on Japan-Guide found it, but the Hatchobori Sardonyx Hotel, seems decently priced and has relatively large rooms for Japan. I'm thinking of trying the new Mitsui (opening in June!) for a few nights as it is brand new and was surprisingly cheap before switching to my splurge hotel.
I've stayed at the Tokyo
Disneyland Hotel. I found it disappointing for a luxury hotel. I didn't think the service/English was as good as other luxury hotels in Tokyo. The only pluses to me were early entry and the 1 day park hopper ticket.
I am not that into Osaka. I go there to see friends and shop, though I am staying there 1 night so I can go to USJ in June 2018. I think Kyoto is a lot more interesting though it does get crowded.
Good luck!