JR pass or separate tickets

Hi,
We (3 adults) are visiting Japan for ~15 days and want to use public transport i.e. trains, buses. Can you advise what is the best pass/ticket for our itinerary?

Day 1 - landing 7 pm at Narita. Narita to hotel in Tokyo
Day 2 - train from Tokyo to Hiroshima
Day 3 - Hiroshima, Miyajima island, etc.
Day 4 - Hiroshima to Osaka (may go to Himeji on this day or Day 3 depending on ease of travel)
Day 5 - Osaka to Nara and back
Day 6 - Osaka
Day 7 - Osaka to Kyoto
Day 8 & 9 - Kyoto
Day 10 - Kyoto to Hakone
Day 11 - Hakone
Day 12 - Hakone to Tokyo
Day 13, 14, 15 - Tokyo. Might do a day trip to Nikko on one of these days
Day 16 - Flight out of Narita

Is it best to get a JR Pass? Should we also get an IC card? Will JR pass cover travel on the metro within each city?
I have read a lot of articles and forum discussions but can't identify what is the best.

Thanks in advance for your help!