A strong side route, but not a free one
Takayama and Shirakawa-go can add mountain atmosphere, older streets and rural contrast. They can also cost more travel energy than expected.
When it is worth it
Choose Takayama if you want a smaller city, food, craft, mountain feeling and a clear contrast to Kyoto and Osaka. Add Shirakawa-go only when the village atmosphere is worth the extra logistics.
When to choose something else
Choose Kanazawa, Hakone or Nikko if the trip is shorter, if transport simplicity matters more, or if your group does not enjoy longer transfers.
Protect the pace
Treat the route as a block. Do not squeeze it between two already intense days. Think about luggage before locking hotels.
When to get personal help
Personal planning is useful if you are choosing between Takayama, Kanazawa, Nikko and Hakone as your side route.