JR Pass or Normal Tickets Tokyo-Kyoto-Hiroshima

Hello JR Pass team!

My partner and I are travelling to Japan in late May to June this year. We were wondering whether it'll be more economical for us to purchase a 14 Day JR Pass or local tickets for our trip. Here's our itenerary:

Day 1: Narita to Shinjuku - is there a direct train from the Airport to Shinjuku inlcuded on the JR pass?
Day 2: Shinjuku to Shibuya(Tokyo West)
Day 3: Asakusa to Akihabara(Tokyo East)
Day 4: Tokyo to Kamakura to Tokyo
Day 5: Tokyo to Nikko to Tokyo
Day 6: Extra day in Tokyo
Day 7: Tokyo to Kyoto
Day 8: Kyoto Full day
Day 9: Kyoto to Nara to Kyoto
Day 10: Kyoto to Himeji to Kyoto
Day 11: Kyoto to Hiroshima
Day 12: Hiroshima to Miyajima to Hiroshima
Day 13: Hiroshima to Kyoto to Tokyo
Day 14: Shinjuku full day
Day 15: Shinjuku to Narita

Hope you can help!

Regards,
B