Does my itinerary need a jr pass?

HI,
We are a family of three including my 10 month old son.
we will be in japan for 8 days in october and i am trying to decide on buying the jr pass or not, and if we do , how to best utilize it considering we have an infant with us .
this is our not yet ready itinerary:
15th oct - evening we have to travel from kansai airport to gion ( kyoto )
16- explore kyoto and nara
17, 18, 19, 20, 21st we need to :
a)explore autumn leaves around nagano, nikko , etc.. any one beautiful area b) visit kawaguchiko area , mount fuji skyline .
c) hakone trip - visit onsen water park there
d) explore tokyo
e) visit hitachi sea side park
22nd - our last day - we have an evening flight from narita ( im even considering squeezing in hitachi park on 22 nd ?

As you see there are 8 days in all, and if i buy a 7 day pass - when should i start using it from? 15th or 16th
also , is a jr pass valid to travel within tokyo and kyoto ?