Planning ahead for September visit

Hello! My daughter and I will be in Japan in September, arriving the 27th and departing October 4th. We arrive in Osaka and spend 3 nights in Kyoto, then go to Tokyo for 4 nights.

We've used the JR Pass before but I want to be sure I plan properly. We'll need to get around between Kyoto, Osaka and maybe Nara, then take the train to Tokyo, and we hope to do day trips to Yokohama & Kamakura, Kawagoe, and Mt Fuji.

Is the JR Pass a good option? Can we get to all these destinations using JR Pass?

Osaka airport - Kyoto
Kyoto - Tokyo (Shinjuku)
Shinjuku - Kamakura - Yokohama - Shinjuku
Shinjuku - Kawagoe - Shinjuku
Shinjuku - Mt. Fuji - Shinjuku
Shinjuku - Narita

Thank you!