Not sure if need JR Pass

Hi,
I'm not sure if I need a JR pass... I'm having a hard time finding what trains and buses and metro lines will accept the JR pass.
I'm flying into Hanedo airport and going to my hotel in Shibuya.
Then I'll be on a day trip to Mt. Fuji. There's an option to be dropped off at Odawara (which I think I can use JR pass to get me back to Shibuya?) Then I'll be traveling to Kyoto and Osaka, then back to Shibuya area. Then to Hanedo airport.
I'm pretty sure Tokyo to Kyoto and Osaka will work with JR pass, but what about around Tokyo and Kyoto and Osaka while I'm there? And if I can use JR pass to get back from the Mt. Fuji day trip?
Thank you for your help.

Mary