7 day pass

My family is traveling to Japan in September. Given the following itinerary, can you tell me if purchasing the JR Pass is economical? We were thinking to activate the pass starting the 16th based on our travels.

Thank you in advance!

Sept. 13 Narita to Tokyo
Sept. 14-15 Explore Tokyo Neighborhoods, i.e., Shinjuku, Asakusa, Shibuya
Sept. 16 Round trip from Tokyo to Hakone
Sept. 17 Explore Tokyo Neighborhoods
Sept. 18 Round trip from Tokyo to Kamakura
Sept. 19 Explore Tokyo Neighborhoods
Sept. 20 -22 Round trip from Tokyo to Kyoto
Sept. 22 - One way from Tokyo to Narita