Help with Japan trip in 4 days

I am flying into Osaka this Thursday and need some advice on what type of Rail Pass I should get.

So I am in Japan for 14 days.
Osaka for 3 Nights, where I want to visit Himeji and Kobe
Kyoto for 4 Nights, where I want to visit Nara and maybe Mt. Koya
Tokyo for 6 Nights, where I want to visit Kamakura, Nikko, and Mt. Fuji.

Now I'm not sure if its worth it to get 14 days or not. I need it to get to Tokyo but that's it.

Any advice on the matter would be super helpful!!!

Are you flying back from Kansai airport as well? The quickest way to answer your question is to check online for the prices of the individual trips and add them together and compare the price with what you would pay for the JR passes.
A couple of things to keep in mind:
+ You can get to Nikko from Tokyo by JR but it takes longer.
+ You can add a few thousand yen a day for your stay in Tokyo if you decide to get around Tokyo by JR mainly (which is pretty doable).