Do I need a JR Pass?

Hi there,

I'll be in Japan for a little bit less than two weeks. My itinerary is as follows:

Day 1 - 5: Tokyo
Day 6 - 7: Mt. Fuji
Day 8 - 11: Kyoto
Day 12: Tokyo

I'll only need to ride the train around Tokyo, from Gotenba station to Kyoto, and from Kyoto back to Tokyo. I will also likely ride the train to and from Haneda airport.

With this in mind, do I need a JR pass? I'm not sure if I would potentially save money by just buying tickets as I go, considering I'm not venturing around the country too much. If I should purchase a pass, should it be the 7 or 14 day pass? And for which days should it be effective?

Thanks so much!