I would like to experience one or two nights in a Ryokan during our upcoming Japan trip.

So far I have booked a two week trip for me and two school-aged kids. I have tentatively booked hotels in Tokyo-Kyoto-Hiroshima-Tokyo, with a plan to do day trips out of each city. The hotel reservations are cancellable and the itinerary is subject to change.

I don't mind which city the Ryokan stay is in, out of the above cities, or in one of the day-trip destinations near each of these cities, which I could turn into an overnight trip including a Ryokan stay.

So far the hotels I have booked vary from (taxes included) 18,000 yen in Hiroshima to to 37000 Yen in Tokyo so that is my price range, although I would prefer to keep it in the low to mid part of that price range if possible. I am interested in a more traditional Ryokan experience rather than a modern-looking building.

Any suggestions would be appreciated. I have done some internet searching and found nothing to appealing in my price range.