Checking on my itinerary with the suitable JR

Hi, I am planning to travel to Japan end of Nov. I am confused which JP pass should I take to travel to some cities.
I am planning to explore Toyo and will be using subway pass but then from Tokyo I plan to spend 1 night at Nikko, 2 nights at Nagano then 1 night to Mt. Fuji, Kamakura just one day trip then back strolling Tokyo.

Please advise which JR pass could cover all those itinerary and do you thing by using JR pass will be cheaper than buying ticket per destination? Can I also use JR in every city I visit or I have to use suica for local transportation within city?

Appreciate your reply and explanation at the soonest for me to start booking hotel and other things.
Thank you!