Tokyo-Kyoto-Osaka-Hakone-Tokyo

Hi,

11April : estimate 2pm arrive Tokyo_narita airport-overnight at Shinjuku area
12April : Kyoto
13April : Kyoto
14April: Kyoto & Osaka half day trip
15April : Hakone
16April : Tokyo
17April: Tokyo
18April: take 605pm flight back home

I planning to get my 7days JR pass.
But since I having 8N7D trip at Japan.
So I plan to active my pass on 2nd day.

Then when 1st day I arrive at Narita airport, any cheaper way/transport for going to Shinjuku station?
And based on all of your guys who have experience travel at Japan, my ltinerary plan is ok?