tour in Japan

Hi there,
we are planing for Aril 2019 ten days vacation in Japan.
The idea is to split the ten days vacation between the following cities:
Tokyo 4 dd
Osaka 2dd
Kyoto 3 dd
Nara in 1 dd
return to Tokyo

based on the upon do you recommend to purchase the 7 days JRP only?

furthermore, is it possible to visit the mount Fuji from Tokyo? If, yes how long it will take the fair?

Tks for your cooperation

reds

gl