Buses/trains included in JR Pass in Tokyo

We plan to visit Tokyo ( Western, Southern, Central, Northern)for 4 days before going to Kyoto. I am confused as to what are the buses that are free to ride using the JR Pass within Tokyo. Please enlightened me. thank you.

The JR passes are only valid on the JR train lines and the monorail. They are not valid on the subways and all the non-JR trains (such as Keisei, Keikyu, Odakyu, Rinkai Line, Tobu, Seibu, Tokyu, Keio, Tsukuba Express, etc.)

The basics of transportation in Tokyo are explained here:
http://www.japan-guide.com/e/e2017.html

Thank you. JR Pass is expensive. How can we maximize the pass since clearly the transportation around Tokyo is not covered by JR Pass?

JR Pass makes sense if you are doing long-distance (meaning inter-city, like Tokyo - Kyoto/Osaka, Hiroshima, etc.) trips on JR Shinkansen trains. You might not need any JR Pass while you are in Tokyo. I don't know how long your total trip is, but if you are doing a return trip between Tokyo and Kyoto/Osaka within a 7-day period, you might consider activating the pass on the day you leave for Kyoto. If you are going just one way from Tokyo to Kyoto, then leaving Japan from Kansai airport, for example, you simply don't need any JR Pass.

We plan to stay 4 days in Tokyo with a side trip to Mt. Fuji then Kyoto for 2 days then back to Tokyo before going home.
Thank you for quick respond.

Last question, is it possible to use the JR pass in Kodama line from Tokyo to Shin-Fuji? Then from Shin-Fuji to kyoto also on the Kodama shinkansen line?

Since you are doing a round trip between Tokyo and Kyoto, then a 7-day JR Pass comes out about even with buying individual tickets.

Yes, JR Pass is valid on JR Shinkansen Kodama trains. Kodama is one type of JR Shinkansen trains :)

Also it is valid on JR Narita Express, so if you are flying in/out of Narita, and if your trip from arrival to departure is 7 days, you can use it both ways too (or one way if your whole trip is 8 days long or something like that).