Checking itinerary and costs

Hello,

Our itinerary is planned :
11/09 -- Tókio - Hiroshima
12/09 - Hiroshima (Miyajima)
13/09 - Hiroshima - Osaka
14/09 - Osaka (Koyasan) Osaka
16/09 - Osaka - Kyoto
17/09 - kyoto - Nara
18/09 - Kyoto - Takayama
19/09 - Kyoto - Tókio
20 - 23/09 - Tokio

My questions would be:
- Using hyperdia my impression was that buying the tickets would be less expensive than using JR Pass. Could you confirm that? - Would you recommend some other places to visit considering that this is our first trip to Japan?

Thank you!