Japan metro

Hi,
City subways are not included in the rail pass. You could use it on the JR Yamanote Line within Tokyo, which goes to many popular places, but obviously not all.
What is more concerning is your itinerary - you write you are going to Tokyo-Nagoya-Osaka (and back)? That doesn't cover the cost of a 14 day rail pass at all. You'd need to significantly increase your travel to get your money's worth. Consider expanding you trip to cover Nikko as a day trip, plus visiting Takayama on the way to Kyoto/Nara/Osaka, and add a side trip to Hiroshima/Miyajima. That would cover the difference quite well.

Good luck.