Sparrow Princess
My ryokan: 2 baths - one with a rotenburo, closed from 8:30 to 15:00. Of everything I visited in Dorogawa, what my place had I liked the most. Rooms are spacious, food is good. The only thing is, if you book through Booking you need to order dinner separately since that option isn't available there - only breakfast is included. And you need to take care of dinner by 4 PM, or you'll go hungry; I had to have cup ramen for dinner. And the main thing - one night was 11k yen. Probably not worth making a special trip, but if you want a budget onsen chill, Dorogawa is a decent option.