14-day or 7-day JR pass?

This is our potential 14 day itinerary for April 2019

Narita -> Tokyo
Stay in Tokyo for 4 days
Tokyo -> Hakone
Stay in Hakone for 2 days
Hakone -> Kyoto
Stay in Kyoto for 2 days
Kyoto -> Nara (day trip) -> Osaka
Stay in Osaka for 2 days
Osaka -> Hiroshima
Stay in Hiroshima for 2 days and travel to Miyajima
Hiroshima -> Tokyo
Stay in Tokyo overnight and flight home via Narita the next afternoon

First off, would love any feedback regarding our itinerary in general
I am trying to decide if we should go for the 14-day pass or just activate a 7-day JR Pass when we travel to Kyoto from Hakone... this would cover us through travel from Hiroshima back to Tokyo but would not include our travel back to Narita airport. My hang up about doing the 14-day pass is that we are not going too far from Tokyo in the first 6 days of our trip since we are staying in Tokyo and Hakone.
Thank you!

Hi!

Personally, I would not switch hotels between Kyoto and Osaka. It wastes an awful lot of time and I'm honestly not sure how much time you are actually spending in Kyoto since you have arrival day (which is not going to be until lunch time at the earliest) Night 1 in Kyoto, go to Nara Night 2 in Kyoto, see some of Kyoto and then travel to Osaka? It is easy enough to get between Kyoto and Osaka and if you leave Kyoto early enough, there are a few Hikari that go straight to Hiroshima. Otherwise, unless you are staying near Shin-Osaka station you're going to need to change trains to get to Shin-Osaka regardless.

I would do the 1 week pass. If you're in Japan for 14 days or less you could just use the following discounted NEX ticket: https://www.jreast.co.jp/e/pass/nex_round.html?src=gnavi It's a pretty good deal on the NEX.

I know many people who prefer the limo buses even though they can cost more simply because they go direct to various hotels and a lot of people use the Keisi to get to and from Tokyo.

Good luck!

7 day pass. Start when leaving Hakone/Odawara.