Is JR pass good for 13 days travelling between Tokyo, Hiroshima, Miyajima, Osaka, Kyoto, Himeji and Hakone?

I'm planning a trip to Japan for 13 days (Mon 7 Oct to Sat 19 Oct) travelling to Tokyo, Hiroshima, Miyajima (day trip), Osaka, Kyoto, Himeji (day trip) and Hakone. I'm not sure if the national JR pass for 14 days ($879 + $29 delivery) is worth it for this itinerary? Thank you for any guidance you can give :-)