We would prefer reasonable price (if even possible.. :)), and a small japanese garden and a public bath would be like icing on the cake.

For regular hotels, what is your budget?

The public bath would be super but that's not a must.

They do have Japanese rooms and large shared bath - I suspect that the Japanese rooms do not come with bathroom, though (I cannot be sure). I've read some reviews and everyone says the building was a bit old... but 14,000 for a double occupancy Japanese room AND close to that area sounds about right, doesn't it? :)

(If you click on the third button from the top in the set of buttons on the left side of the page, it takes you to the Japanese chart for the rooms. The ones marked with a star have no bathroom.)

So... I hope the original posters can live with a bathroom they have to go out of your room to reach (just down the hall probably)...

It can sometimes be hard to locate information on whether Japanese-style accommodations have bathrooms. Most of the time, their web sites or Rakuten/Jalan listings are pretty clear, but sometimes you have to dig and dig, especially when some of a property's rooms have bathrooms but others don't. In this case, it was fairly easy to find but you can hardly be faulted for missing it! It surely took some digging just to find the hotel.

Ryokans are usually associated with hot springs and mountainous rural areas, or alternatively as above cheaper accommodation in more suburban areas, so don't be surprised if you don't find what you are looking for- especially with your budget, which is low for the area.