Ryokan are more traditional Japanese-style accomodation. Straw "tatami" mats on the floor, perhaps a scroll on the wall, sleeping on futons, often serving Japanese style breakfest in the morning.
It's a great chance to get into a bit more traditional Japanese culture during a visit to Japan. Wear a thin cotton robe, enjoy a late night bath, pad around in slippers and sleep on the floor. Most Japanese people may not live like this now, but not too many generations back these ryokan-rooms resembled most housing in Japan.
Ryokans vary in their traditionalness - some are quite modern and concrete, some are in old buildings with wood everywhere. Many of the best are small, run by individuals or families who will look after you and make recommendations for your time travelling.
At Hiragen Ryokan the exposed wood and tall ceilings will put the zap on your brain.
Kimi Ryokan in Ikebukuro, Tokyo, is a good cheap stay.
My favourite ryokan in Tokyo is Taito Ryokan because the proprietor Keiichi is a warm wonderful fellow. It's super-cheap and a little bit run-down last I saw. People with a bit more money might enjoy Shigetsu Ryokan nearby, with top-floor marble baths overlooking a large Kannon temple. But the staff is nearly belligerant in my experience.
Try looking with the Japanese Inn Group.