Using JR passes on local transport

We're travelling to Japan later this year. Arriving Tokyo where we will spend 5 nights (visit will include a day trip to Hakone). Then on to Matsumoto for 2 nights, Kanazawa for 3 nights, Kyoto for 5 nights, Osaka for 4 nights, and Hiroshima for 4 nights before heading to Tokyo airport and flying home. We will be in Japan for 23 nights.
I was planning to get 21 day JR passes as we won't need them immediately we arrive - was going to activate them for the Hakone day trip. Is it worth getting passes for this trip - we plan to spend time exploring each city, using local transport - am I right in assuming we can use the passes locally? Thanks.