Do I buy the JRP?

Hi,

We arrive in Tokyo on the 19th December and returning to London on the 5th January.(18 days in total) This is our itinerary, please could you let me know if it's the best thing for us to do.

Tokyo - Kyoto (4 nights) - Tokyo (4 nights) - Hakone (1 night) - Osaka ( 5 nights) - Hirosnima ( 3 nights) - Tokyo - London

I am totally unsure what is the best to do.

Many thanks

Carly