Should I Get a JR Pass?

Hello

I have 8 days in Japan and am wondering if I do need the JR Pass at all?

I intend to stay 3 days in Tokyo, 2 days at Mount Fuji and a further 2 days in Kyoto before making my way back to spend a night at Tokyo. I have a mid-morning flight so I intend to stay somewhere nearer to Narita Airport.

I presume if I do get the pass, it will be the 7-days and if so, I wouldn't be able to activate it for the first day in Tokyo which means I have to find another way to get from Narita Airport to my hotel in Shinjuku.

And will I be able to use the JR pass at all travelling around Tokyo? Will it be convenient to travel at all on the JR Pass to major attractions like the Meiji Shrine, Imperial Palace,Tsukiji, etc?

I will be able to use the JR pass to travel to Mount Fuji (Mishima) and then onward to Kyoto and return back to Tokyo. And possibly from my hotel to Narita airport.

But is the cost savings worth it? And does it save me both money and time?

Thank you.