Does it save?

Hi. We'll be travelling to Japan for 10 days. To maximise the use of the 7day JR pass we thought to only use it when we left Tokyo on Day 4. Checking your fare calculator, it does not save any cost. I have however not added in local travel. The following is a rough itinerary

Day 1: Shinagawa - Hakone
Day 2: Hakone - Kyoto
Day 2-4: explore Kyoto
Day 5: Kyoto - Osaka
Day 6:Osaka - Nara - Osaka
Day 7: Kansai Airport

Without internal city travel, the total fare is roughly USD 200. Do you think internal travel in Kyoto and Osaka be worth the extra cost?

Thanks!