JR pass

Hi
Sorry I know this has probably been asked a thousand times before but I am a little lost to whether or not a JR pass would be better to use while we are in Japan. It is our first time and I have been trying to work out the train systems and what is covered on the JR.

We are looking to stay in Tokyo in Shijuku, Shibuya or Ginza for 3 nights then heading to Osaka and Kyoto.
I am looking at staying somewhere in each city close to the train stations for easy access to go between citys. But lookig at the Hyperdia I see there are a few links? maybe not covered by the JR?

If we were to go to Osaka from Tokyo and Kyoto then back to Tokyo is the JR going to be better so that I can also use it for Airport transfers?

If we only stay in Tokyo will we even need a JR pass?

Thank you for your time

Karina