You will find no shortage of temples and shrines in Kyoto - enough to last over a year. If you want to see the more traditional areas, there is Higashiyama, not to mention in the evening Pontocho and Gion.
Kanazawa also has its chaya areas but the crown jewel of the city is the Kenrokuen Garden - an absolute must see.
Takayama has its preserved old streets, but they are overrun in the day with tourists, and the shops mostly sell tourist junk. You might want to go up the tracks to Hida-Furukawa - much the same vibe, with a lot fewer people. The Hida-Takayama Folk Village is also excellent. Shirakawago also is famous preserved houses, though it too is overrun by tourists in the day. You might want to go to the lesser crowded villages like Gokayama. Nara is also a must see place, especially the Todaiji Temple and feeding the deer.
If you still want more, there is Miyama, about 30km north of Kyoto.
We are in Tokyo for 3 days,Kanazawa for 1,then to Shirikawa,and on to Takayama.
To Kyoto for 2 days,Hiroshima 2 days then to Nara finishing at Osaka for 2 days.SO our joy would be seeing Japanese old Shrines,Gardens ,Giesha areas,Sumo practise area knowing that the Sumo season will be over when we arrive and leave.Educating ourselves and enjoying Japanese food.
But No Electronic,shopping if so only the Authentic Japanese areas,No US styles for us.
We are on a Budget ,so suggestions welcomed for Tokyo,Kyoto and Osaka,the rest are largely taken Care of.
Which part of Japan are you talking about?Nikko for shrine
Shirakawago for local citizens houses.