when to activate, for maximising Jr Pass ?

Hi, we are visiting Japan from 15May-1june

Day 1. Kansai to Osaka, Shinsaibashi-
Day 2. Osaka
Day 3. Osaka
Day 4. Osaka - Hiroshima
Day 5. Hiroshima
Day 6. Hiroshima- Kyoto
Day 7. Kyoto
Day 8. Kyoto
Day 9. Kyoto- Hakone
Day 10.Hakone
Day 11. Hakone-Shinjuku, Tokyo
Day 12- Day 18. Tokyo -Narita Airport

We have brought the 14days pass, was wondering when should we activate the pass to maximise the usage. Would we be using more of JR- railway during Osaka or Tokyo?

Itinerary for Osaka..
Umeda Sky Building
Shinsaibashi
The Momofuku Ando Instant Ramen Museum
Hankyu Minoo Station
Osaka Castle

Itinerary for Tokyo and side trip to yokohama.

Yokohama, pier, ramen museum
Tokyo Tower, Onarimon Station
Tsukiji Market
Harajuku
Odaiba rainbow bridge

Awaiting for your reply! =)