Upvote:8
The obvious answer is Kyoto, including the famous Gion (祇園) district. You should be able to stroll through streets that mostly feature traditional Japanese architecture.
While I never went to Kanazawa myself, from my research, it does feature many areas that feature traditional architecture, including the Higashi Chaya (東茶屋街) and Kazue-Machi (主計町) districts.
Note: While in Kanazawa, you should also visit Kenroku-en, one of Japan's three most famous gardens.
As for Takayama, I recommend visiting Hida folk village. This is in a totally different style than Kyoto and Kanazawa, but it does feature a very well preserved village. Not quite "everyday" architecture as it's an open air museum, but interesting nonetheless.
If you can afford to spend a night there, check out Shirakawago as it is possible to rent a room in one of the traditional thatched roof houses.
Lastly, I have a few recommendations of things you might enjoy:
The Takenaka Carpentry Tools museum in Kobe gives a very good understanding of the underlying principles that make traditional Japanese architecture what it is. Plus, it's less than 5 minutes from the Shin-Kobe shinkansen station, so it makes for a great stop. Check out this question for a more detailed explanation.
The Tokyo Edo Museum has a very nice (historically accurate) full size reconstruction of a Kabuki theater.
The Osaka museum of Housing and Living features a full indoor reconstruction of an Edo period town.