Hi there!
While you'll save ¥2,460 if using a 7 day JR Pass from day 1-7, you'll save around ¥7000 (basic) if you opt for the 14 day pass with your itinerary as listed:
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Narita airport terminal 1 > Osaka: ¥15,850 (272mins, 635km)
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Osaka > Kyoto: ¥540 (29mins, 42km)
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Kyoto > Nara: ¥690 (44mins, 41km)
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Nara > Kyoto: ¥690 (44mins, 41km)
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Kyoto > Osaka: ¥540 (28mins, 42km)
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Osaka > Nagoya: ¥6,380 (67mins, 190km)
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Nagoya > Takayama: ¥6,070 (150mins, 166km)
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Takayama > Otsuki: ¥15,330 (355mins, 580km)
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Otsuki > Tokyo: ¥2,860 (76mins, 87km)
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Tokyo > Narita airport terminal 1: ¥3,140 (58mins, 79km)
JR ticket cost: ¥52,090 for 10 legs
As a suggestion, how about modifying your trip so that you spend a little more time in Tokyo and then take a 7 day trip out of Tokyo? 2-3 nights in Takayama may be a bit much. How about something like:
Day 1: Tokyo
Day 2: Tokyo
Day 3: Osaka
Day 4: Kyoto
Day 5: Kyoto/Nara
Day 6: Takayama
Day 7: Shirakawago (day trip from Takayama)
Day 8: Hakone/Kawaguchiko
Day 9: Hakone/Kawaguchiko + Back to Tokyo
Day 10: Tokyo
Day 11: Tokyo
Day 12: Tokyo to Narita
Here's the cost breakdown for the long distance travel:
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Tokyo > Osaka: ¥13,950 (194mins, 556km)
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Osaka > Kyoto: ¥540 (29mins, 42km)
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Kyoto > Nara: ¥690 (44mins, 41km)
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Nara > Takayama: ¥10,010 (254mins, 356km)
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Takayama > Odawara: ¥16,410 (294mins, 559km)
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Odawara > Tokyo: ¥1,450 (36mins, 83km)
JR ticket cost: ¥43,050 for 6 legs
This plan would let you use a 7 day JR Pass for your long distance travel, and then free you up to use cheaper travel around Tokyo (I recommend unlimited Metro passes for Tokyo). If you do go for this option, you should use either the [Narita Express + Suica] or Keisei Skyliner + Metro Pass deals to get to/from Tokyo from Narita. Though the JR Pass is valid for JR lines in Tokyo, it is not valid for travel on the metro in Tokyo, Osaka, Kyoto etc, so you will need to purchase individual tickets for this.
Hope this helps!
