Best Value JR Pass Use

Hi!

I'm travelling for 13 days to Japan in May. Itinerary summary is:

Day 1 - Fly into Haneda; travel to Kyoto
Days 2-5 - Kyoto area (incl day trips, e.g. Nara)
Day 6 - travel from Kyoto to Hiroshima
Day 7 - Hiroshima
Day 8 - travel from Hiroshima to Tokyo
Days 9-13 - Tokyo area (incl maybe a day trip or two, e.g. Kamakura)
Day 13 - Fly home

I've heard that a JR pass isn't really that relevant in Tokyo, that I'll be needing a subway/metro pass - is that true?

I wondering if I should get a 7-day JR pass instead of a 14-day one. But if I get the 7-day pass, one of my long intercity trips isn't covered.

There is the option of buying a 'Oneworld Yokoso Visit Japan Fare' airfare as my international flight is with a Oneworld airline & I qualify - this will cost me around 10,800 Yen from either Tokyo>Kyoto or Hiroshima>Tokyo.

I'm essentially looking for the most cost-effective option for my travels. Any assistance is appreciated!

Thanks!
M