the three nights in Takayama.One day will be getting there,so it only leaves two days.
Of those,one for a walk around the town and a visit to the few sights there,and one for a day trip (Shirakawago as you suggested,for example) is fine for me.Its not the greatest place in Japan but its a nice example of a well restored smaller city.
Certainly you will find plenty of tourists there.As you will in most of those places...Japanese tourists if not foreigners (main temples of Kyoto,Kamakura,Nara etc.)Don't count on seeing snow,though it is certainly possible in December.












