Hi there!
Looks like a great trip!
As 21 day JR Pass is ¥57,700, you'll need to spend at least this on JR tickets for a rail pass to be economical. Lets take a look at your travel over the 21 day period 19th March - 8th April as this is the period with the most travel:
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Tokyo > Odawara: ¥3,840 (35mins, 83km)
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Odawara > Kyoto: ¥11,950 (160mins, 429km)
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Kyoto > Sagaarashiyama: ¥230 (16mins, 10km)
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Sagaarashiyama > Kyoto: ¥230 (16mins, 10km)
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Kyoto > Inari: ¥140 (5mins, 2km)
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Inari > Kyoto: ¥140 (6mins, 2km)
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Kyoto > Osaka: ¥540 (28mins, 42km)
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Osaka > Takayama: ¥10,610 (223mins, 357km)
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Takayama > Kanazawa: ¥4,380 (186mins, 148km)
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Kanazawa > Takayama: ¥3,980 (161mins, 148km)
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Takayama > Hiroshima: ¥16,110 (356mins, 694km)
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Hiroshima > Miyajimaguchi: ¥400 (26mins, 21km)
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Miyajimaguchi > Hiroshima: ¥400 (28mins, 21km)
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Hiroshima > Tokyo: ¥18,250 (292mins, 894km)
JR ticket cost: ¥71,200 for 14 legs
As you can see you'll make good savings with a 21 day JR Pass so I can certainly recommend it. You'll also be able to use it a little around Tokyo on the 8th (here's a map of JR lines in Tokyo for reference). Please note that for Hakone the JR Pass will get you as far as Odawara. From Odawara I recommend you purchase the 2 day Hakone Free Pass which will cover all your travel upto and around Hakone and include some discounts and free access to attractions.
For your travel to and from the airport and around Tokyo I recommend you purchase the following discount tickets:
- 1 x [Single Narita Express + SUICA prepaid travel card]. This will get you into town and also give you ¥1500 of travel value on all trains and buses around Tokyo. You can recharge it at all stations.
- 1 x Single Keisei Skyliner + 2 day metro pass. This will get you back from Ueno to Narita direct and also include 2 full days of unlimited Tokyo metro travel.
- (optional) further 1 or 2 day metro passes. To add further cheap unlimited Tokyo subway to your travel options. The 2 day passes work out at ¥490/day which is really good value if you do more than a few subway trips.
Note that these are only available for purchase at Narita airport so be sure to stock up on arrival. There is a return version of the Narita Expres + SUICA package, but it is only valid for use within 2 weeks so will not be suitable for you I think. Also, the Keisei Skyliner departs from Ueno (Keisei Ueno station) so it will be really convenient for you I think.
You can look up precise train timetables and costs at the Hyperdia travel planning website and learn how to use Hyperdia for JR Pass holders through our video blog.
Hope this helps!