Any help, please?

Hi there,

i am going to Japan the 5th-24th of oct.
Will a 14 day jr pass be cost efficient for me?

5-10th in Tokyo
10-12 mt. Fuji
12-17 Kyoto (one day travel to Osaka by train)
17-19 Naoshima
19-24th Tokyo.

I will start the pass from the 10th ending on the 24th.
In tokyo we are planning using the metro. is that included in the Jrpass?

Thanks a lot. :)

/Regitze