Hi there!
As a 7 day pass is ¥28,300 you'll need to spend more than this on individual JR tickets to make a rail pass cost effective. Lets take a look at your individual ticket costs assuming you will visit Lake Kawaguchiko for Mt Fuji:
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Narita airport terminal 1 > Tokyo: ¥3140, (62mins, 79km)
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Tokyo > Otsuki: ¥3060, (84mins, 87km)
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Otsuki > Tokyo: ¥1450, (102mins, 87km)
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Tokyo > Maihama: ¥210, (15mins, 12km)
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Maihama > Tokyo: ¥210, (16mins, 12km)
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Tokyo > Kyoto: ¥13420, (164mins, 513km)
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Kyoto > Nara: ¥690, (45mins, 41km)
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Nara > Tokyo: ¥13950, (223mins, 555km)
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Tokyo > Narita airport terminal 1: ¥3140, (58mins, 79km)
TOTAL: ¥39270 for 9 legs
- 07 day rail pass (¥28,300) saving: ¥10,970
Itinerary analysis
As your itinerary is for 9 days I recommend the following tickets:
- [Narita Express + Suica prepaid card] (single) from Narita to Tokyo
-
7 day JR Pass for use from day 3 to day 9.
The Narita+Suica deal will give you simple travel into and around Tokyo for the first few days of your trip on both Narita Express, subway and JR lines in and around Tokyo. Effectively you get ¥1500 of free metro travel on a prepaid card with this offer.
The 7 day JR Pass will then cover the majority of your travel (see below for exception) until you leave Japan, resulting in a total minimum saving of ¥7830.
Tokyo and Mt. Fuji
You can use the JR Pass for travel between Tokyo and Narita on the Narita Express and can also use the JR Pass around Tokyo. Here's a map of JR lines in Tokyo for reference.
For Mt Fuji (Kawaguchiko) you can use the JR Pass to get most of the way to Otsuki station. Here you should change to the (non-JR) Fujikyu line for the final trip up to Kawaguchiko. As this final leg is not JR you will have to pay for this ticket (¥1,110 each way per adult). Here is a sample itinerary for you.
Hope this helps!