If you like the traditional sides of Japan and have already seen a lot of temples, yet might not have the time or confidence to travel in rural Japan by yourself (English is rare there), a visit to the UNESCO heritage villages of Shirakawa-go and Gokayama is highly recommended. They are located in the area of Hida, near Takayama, which is also a beautiful town worth spending a few days in. There are a few different small villages, with Shirakawa-go being the biggest. Suganuma is another one we visited, which was a lot more quiet and peaceful, yet also had some small museums and souvenier shops.
This area is one of the most remote of Japan's main island of Honshu. The villages are only reachable by bus or car. The new tunnels built between Takayama and the villages have cut the travel time to about an hour and a half - before it took 3 - 4 hours or more to get there, and it winter, the villages were often completely cut off from the world. The villages are famous for their special thatched roof houses, which are several stories high and traditionally were heated by an open fire burning in the lower level. The smoke eventually turned the wood on the inside of the building black, which supposedly helps to preserve the material.
The thatched roof has to be renewed every couple of years - and this is the main reason of the UNESCO status, as the material for thatching has become very rare today and has to be brought from other areas of Japan. This means the average price for a new roof, including labour, is around $200.000!
Several of the buildings in the villages can be visited for small entry fees. I especially recommend the temple and the biggest of the thatched houses in Shirakawa-go, which houses an exhibition on the area. The temple museum focuses on the local rice wine festival, and you can even try some of their local rice wine (like a very high alcohol Korean magkeolli) for free.
Of course, this being Japan, there are also local delicacies! Everywhere sells chestnut ice cream, but the best local product is their pickled smoked burdock (gobo) - I've not seen this anywhere else in Japan and it's incredibly tasty, a bit like BBQ sauce. Don't forget to get some for Japanese friends :)
If you have some more time, several houses also offer a homestay. I'm not sure if they are English speaker friendly, but I've never heard of anybody receiving anything but kindness and hospitality in rural Japan - so it shouldn't be a problem if you don't speak Japanaese.
You can visit the villages with a rental car, but I do recommend getting a good tour guide, who can make the hstory and traditions of the area, including the many handicrafts and festivals unique to here, come alive for you.
We visited on a tour with Nohi bus, and it turned out that three of us had the English speaking guide to ourselves. The lady was outstanding - I've never met a tour guide who knew so much about a place and could answer even the most pesky (and critical) question. She even went out of her way and tried to get us another bus ticket back in Takayama, when the bus we wanted to get on was sold out.
Nohi bus is the local bus company that runs buses from Shinjuku to Takayama, some also continue to the villages, and on to Kanazawa City as well as all the way from Kanazawa to Kyoto and Osaka.