7 or 14 day JR pass?

Hi,

I'm trying to work out which JR pass makes the most sense for our upcoming 12 night holiday. We didn't take this into account when booking accommodation unfortunately, our itinerary is as below:

20th April arrive 9pm Haneda airport, staying in Ginza.
21st April travel to Osaka for 2 nights (? day trip to Himeji Castle or Kobe in here)
23rd April travel to Miyajima island, staying overnight Hiroshima.
24th April travel to Kyoto for 3 nights (? day trip to Nara in here)
27th April travel to Hakone/Mt Fuji stay overnight
28th April travel to Tokyo, staying in Tamachi for 4 nights with a day trip to Nikko
2nd May depart Haneda airport 8pm.

I can't decide if we should buy a 7 day pass, activate on the morning of the 21st, knowing we will then have to pay separately for the travel from Hakone to Tokyo and travel around Tokyo/any day trips we do, or go for a 14 day pass.

Any advice would be greatly appreciated.
GB