JR Pass right for us?

Hi there,

Our itinerary is as follows:

1. Flying into Tokyo Haneda airport then travelling to Shinjuku, Tokyo.
2. Staying in Shinjuku, Tokyo for 4 nights and will be visiting Mount Fuji on one of our days in Tokyo.
3. Travelling from Tokyo to Kanazawa and staying in Kanazawa for 4 nights.
4. Travelling from Kanazawa to Kyoto (Sanjo-Sagaru) and staying in Kyoto for 4 nights.
5. Travelling from Kyoto to Osaka and staying in Osaka for 2 nights.
6. Flying from Osaka to Okinawa main island (chatan cho) and staying there for 4 nights.
7. Flying from Okinawa mainland island to Tokyo Narita airport and spending 2 final nights in Kabukicho, Tokyo.
8. Flying out of Tokyo Narita airport back to the UK.

We are staying for 20 nights in Japan. My question is, should we get a JR pass and if so, should we get it for 3 weeks?

Many thanks for your time and reading my question.

Greg