JR pass or not..

Hi I will be arriving into Osaka Kansai international airport in February and intend to spend 4 days traveling up to Tokyo in readiness for the Tokyo marathon 1 week later.

-I will visit Kyoto 2 nights...using the Haruka express train - Then onto Hakone national park / Mt Fuji 1 night using the bullet train ( to Odawara I guess) -Then into Tokyo on the bullet train where I will spend 5 nights before I fly back home.

Will it be worth my while purchasing a JR pass for these 3 train trips?

From what I can see it looks cheaper to pay for the 3 individual journeys but don't know if this is a pre booked tourist price tickets purchased in advance or if these are the prices I will pay at the train station.

I see that the JR rail pass doesn't allow you free travel on the metro / TOEI lines :( As I will be just sightseeing in Tokyo, I guess it will be easier to just purchase an unlimited dailyTokyo metro pass for the free Metro travel.

Please can somebody advise?

Kind regards