Should I purchase the JR Pass for this itinerary?

I am so happy I found this forum, I've been breaking my head over which railways accept the pass and which do not. In a 7-day period I will visit the following cities
Hakone - to Osaka - one way trip
Osaka to Nara - round trip
Osaka to Kyoto - one way trip
Kyoto to Utsunomyia - one way trip
Utsunomiya to Tokyo - one way trip
According the the JR Fare calculator, I can save a bit ($50 USD) if I purchase the 7-day pass. Can anyone help confirm this?
Thanks so much!