JR Pass for just 5 main trips + side trips

My second trip to Japan this time with my wife and we will be traveling Tokyo- Kanazawa-Takayama-Hiroshima-Kyoto-Tokyo and of course within those cities do you think this would be worth the JR 21day pass, our trip is 23 days but traveling 21 of the days.
Thanks

14 day pass definitely, but I don't know about 21 day. Check your itinerary on Hyperdia and total the train trips' costs to see if it's worth it.

Unlikely a 21 day pass would pay-off.

You can get a rough estimate on the main legs at https://japancustomtours.co.nz/railpass.htm If it works out close then you could check the individual legs on Hyperdia.

The main legs will costs about 2000yen short of the 21 Day JR Pass. So the question is: Would you pay 2000yen for the convenience of flashing your JR Pass and going through the gantry like a boss, cut through train stations instead of walking around it, and queuing up to buy tickets.

Also it depends on how many days you are spending in each city.
For example, spending 7 days in Kansai, 4 days in northern chubu, and 3 days in Hiroshima prefecture is a 14 day JR Pass. That gives 7 days in and about Tokyo. Get the Nikko and Fuji Hakone Passes for these days. So why the need for 21 days pass?

Unless of course, during the 7 days of Tokyo you plan to day trip to Nikko, Kamakura, Nagano, Karuizawa, and Kusatsu.