Is a JR pass worth it for this trip

Hi,
A 7 day pass would pay off for the long distance travel. A 14 day pass would not, without extending your trip to Hiroshima/Miyajima, or Takayama, for example. For seeing Mt Fuji you can go to Hakone or the Fuji 5 Lakes area - the Pass can get you there part of the way. But there are other non-JR regional passes for those areas. For within Tokyo you can use the Pass for the JR Yamanote Line, which goes to many popular places, but not all. The Pass does not cover city subways, but they are not expensive.

Good luck.