Looking like Kanazawa then!
We'll be coming from HKG and it seems the best way to do this would be to fly to NGO and then get a
Hokuriku Furii Kippu (JPY 15,000/person; 4 day validity; covering a return from Nagoya to the Hokuriku area on certain trains and travel within the Hokuriku area).
The ticket's conditions of use seem to require careful reading, e.g. at first glance, it seems I must reserve seats for the journey to Hokuriku. It also says that I can have a "stopover" in Takayama but it's not entirely clear whether a "stopover' means > 24 hours or not (since if we can a night there would be nice):
You may not make stopovers except for within the JR Line unlimited travel area and at Gero, Takayama and Hida-Furukawa stations. If you get off the train at other stations on the way, your ticket will become invalid for the remaining portion of your trip and you will not be able to board the train again.