Hi there!
Given your current itinerary lets have a look at your total ticket cost:
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Narita airport terminal 1 > Tokyo: ¥3,140 (62mins, 79km)
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Tokyo > Kamakura: ¥2,100 (47mins, 51km)
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Kamakura > Tokyo: ¥890 (54mins, 53km)
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Tokyo > Nikko: ¥5,630 (121mins, 150km)
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Nikko > Tokyo: ¥5,630 (117mins, 150km)
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Tokyo > Kyoto: ¥13,420 (164mins, 513km)
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Kyoto > Osaka: ¥540 (28mins, 42km)
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Osaka > Tokyo: ¥13,950 (194mins, 556km)
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Tokyo > Narita airport terminal 1: ¥3,140 (58mins, 79km)
JR ticket cost: ¥48,440 for 9 legs
As you can see you'll make great savings with the 14 day option. As the difference between a 7 and 14 day pass is ¥16,800, you'll need to spend at least this in addition to the 7 day pass in order to make a 14 day pass worthwhile.
Looking at the costs, if you could move the trip to Nikko to the 14th, or return to Tokyo a day earlier and start your JR Pass on the 13th, your non-JR Pass costs will be ¥9270 and so it will be worthwhile. If you cannot change these dates of travel, you'll also need to pay for the Nikko return, which will push up your non-JR Pass costs to the level that a 14 day pass is worthwhile.
Hope this helps!