Places accessible by train and have traditional buildings:
Kamakura is in Kanagawa Prefecture. There are lots of shrines and temples because Kamakura used to be the capital of Japan for a period of time. There are also traditional houses and accommodations or restaurants or cafes that use those houses after renovation. Such as Kamakura Guesthouse.
Sawara is in Chiba Prefecture, the place is close to Narita Airport so you can stop by here if you are using Narita Airport before you come to Tokyo. Sawara is a beautiful place with traditional buildings along the river. Boat cruise on the river will feel as well as walking around the traditional buildings and look at them. There are few ryokans (traditional inns) in the area. The sightseeing association website is only in Japanese but you can see the pictures: