7 day vs. 14 day pass

First off, you do a great job in answering people's questions!

I am flying into Narito and will stay in Tokyo for 2 nights either in Chiyoda or Minato.
We are young adults and are able to walk for miles and interested in tourist sights.

Will we rely heavily on transportation if staying in Minato? We want to see as much of Tokyo as possible.

After Tokyo, we will use the JR Pass to travel to Osaka, Kyoto, Nara, Kobe all in 7 days.

We are trying to save money by not activating the JR pass until we leave Tokyo. But we are not sure if we will end up spending more money on trains in Tokyo getting around.

Should we get the 7 day pass or the 14 day pass? Thanks so much!