Name of the town you want is Kanazawa
Since Nagoya is your start point...
Inuyama - lovely castle and the wonderful Meiji Mura Historical Architecture park - lots of notable buildings that made it through WWII were transported here
A visit to Tsumago and Magome - you can travel on to Shirakawa go and from there get a bus to Kanazawa. From Kanazawa there is a train back to Kyoto.