Takayama is a very convenient base for day trip to Shiragawa-go and Kamikochi, or spend the night at Hirayu Onsen for relaxing.
The Takayama old town is not really my cup of tea, as it's row of old shops with some local specialty like wine and miso.
The morning market is a nice stroll, but nothing too spectacular. Bought some fruits, souvenirs and street snacks.
The interesting thing about Takayama is its river, crystal clear with plenty of red koi in it. Saw some kids feed them with some fish food.
The Hida Folk Village has a large koi pond with fish food for feeding, some traditional toys to play with and 200+ tree hatched houses as museum (the same kind of houses in Shiragawa-go, but it's unoccupied and you have go in). There is also a temple bell where you can knock it with a ram, and make a wish.