After Takayama, we visited Shirakawago. Shirakawago is located in the remote mountains of Gifu Prefecture. You can get here by taking the Nohi bus at Takayama JR Station (about 50 minutes one way – took me longer due to heavy traffic that day). The bus takes you right to the main attraction of Shirakawago, the Ogimachi Village. It was one of the most unique and picturesque places I’ve ever visited in Japan. It is a bit difficult to access, but if you are visiting Takayama, a side-trip to Shirakawago is highly recommend.
Shirakawago is best known for the gassho-zukuri farmhouses. Declared a UNESCO World Heritage Site, some farmhouses are more than 250 years old. Some of the houses have been turned into restaurants and traditional Japanese style lodgings, and you can request to stay overnight via Japanican: http://www.japanican.com/en/hotel/list/16/160503/?aff=EXJ
Some houses are home of the villagers and are not for commercial use. We only stayed here for a couple of hours, but if you really want to explore, the best is probably to spend a whole day and then stay overnight.