JAPAN RAIL PASS OR NOT?

Helo
We are in Japan from Oct 3 - 13 for the Rugby World Cup arriving at Haneda airport at 21.35 hrs, staying in Tokyo for 4 nights sightseeing and the rugby on 5 October. On 7 October, catching the Shinkansen to Kyoto, spending 4 nights in Kyoto ( visiting Osaka/Nara) then catching train/Shinkansen back to Tokyo for 2 nights ( rugby in Yokohama on 12 October) then back to Haneda on 13 October..
This is our first visit to Japan and, based on the above itinerary, we are not sure not sure whether to get a 7 day pass.
Also, if we get a 7 day pass, which day would be best to activate it?
Does it cover the train/bus fro Tokyo to Haneda?

Many thanks for your advice!