JR Pass - Yes or No

Hi,

Travelling to Japan for the duration of 21 days - 1st Oct to 20th Oct.

1st Leg - Tokyo (2nd Oct - 4th Oct) - Exploring Shibuya + Shinjuku
2nd Leg - Osaka - Kyoto - Hiroshima (5th Oct - 12 Oct)
Planning to stay in Osaka and Cover - Kyoto - Hiroshima - Nara and Osaka
3rd Leg - Tokyo (13th Oct - 20th Oct) - Exploring Ginza, Ueno, Asakusa, Kamakura & Mt. Fuji.

Wanted to understand, if it makes sense to buy JR Pass. And if yes which one will be the most efficient. Thank You!