Is a JRP Worthwhile for my Trip?

Hi,

I've put much thought and research into this, but I'm now getting mixed messages and wondered if anybody could lend some advice.

My itinerary is a little messy, as I couldn't figure how to arrive in Kansai airport and depart from Narita (this is my first holiday alone - or even without parents!).

Basically:
Day 1: Arrive at Kansai and travel to hotel.
Day 2: Day in Kyoto (1)
Day 3: Day in Kyoto (2)
Day 4: Day in Kyoto (3)
Day 5: Check out of Kyoto - TRAVEL TO TOKYO
Day 6: Day in Tokyo (1)
Day 7: Day in Tokyo (2)
Day 8: Check out of Tokyo - TRAVEL TO KYOTO (I know >_<" )
Day 9: Fly Home.

I'm considering a trip to Nikko from Tokyo, and I've deliberately not planned so much for my time in Kyoto, so that I'm not rushing around - BUT I may venture out to surrounding areas whilst i'm there.

Could someone please confirm when I would need to activate a 7 day pass, and if it would even be cost effective, please? From my understanding (for example) if I were to activate my JRP at 23:00 on day## - that would count as a one of the 7 days, despite only having used it for an hour... in which case, am I right in thinking I'd best activate it on Day 2?

I hope this is clear. Any clarification and advise will be greatly appreciated, thank you!