Is the rail pass suitable for my itinerary

Hi!
My name is name is Angelika and we are travelling in April to Japan. I have put following itinerary together and I am wondering if I am better off buying a JR pass or separate tickets for my plans. As local transportation in Tokyo or Kyoto is (Subway..) is not included. Also our days are very spread out. Ireally appreciate any advice and expertise.

Itinerary 16 days
08-13 April Tokyo, arriving at Narita, City sightseeing , 1 day a guided tour to see Fuji San and the lakes

13-15 April Kanazawa

15-19 April Kyoto: City sightseeing, day trip to Nara and possibly one day Osaka

19-22 April Hiroshima: one day in the City on day ferry over to the Island

22 April back to Tokyo
23rd departure ex Narita.

Also apparently the Shinkansen from Hiroshima to Tokyo (Nozomi) is not included in the pass.

Thanks for any assistance I am a little worried about making the right choice!

Tomo Arigato
Greetings from Vienna Angelika