Tokyo city travel

hello Daniel, i am travelling to Tokyo city from Narita to Rappongi where i am staying then spending 5 days travelling around Tokyo visiting such things as fish markets, Ueno zoo, Oedo Onsen Monogatari, Ryogoku Sumo Stadium plus some other areas in Tokyo city.

i have heard that the NEX Tokyo Direct ticket is the ticket i should buy to travel from Narita to accommodation in Rappongi as it is very cheap for foreigners.

I am then catching the bullet train to Kyoto and spending two nights in Kyoto before catching a train from Kyoto to Osaka airport.

the question is, should i buy a 7 day Japan Rail pass for the Narita- Rappongi trip, Tokyo-Kyoto trip, Kyoto-Osaka trip, and can i use the rail pass for my Tokyo city train travels?
thank you in advance
Cath