Hi there,
I think you've got the locations arranged in a good order. Arguably you could spend less time in Osaka as it features heavily at the start and end of your trip, but it very much depends on your overall aims - explore a wide area vs staying in a place and capturing a slice of Japanese life. If you did decide to do more exploring, your chosen cities are great starting off points for a lot of day trips, so using them to anchor your holiday is a good idea.
To cover all of the locations you list, you'll need to use the nationwide pass - I'll calculate the costs from the point of leaving Osaka to when you return to the city as this encompasses your most long distance travel. For travelling to Osaka from the Airport and some subway travel you can look into the JR-West Haruka+ICOCA deal, the Surutto Kansai Pass, or just purchase airport/subway tickets as needed.
Lets see if your long distance travel will cost more in standard tickets than a 21 day JR Pass:
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Osaka > Hiroshima: ¥10,150 (104mins, 345km)
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Hiroshima > Miyajimaguchi: ¥400 (26mins, 21km)
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Miyajimaguchi > Hiroshima: ¥400 (28mins, 21km)
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Hiroshima > Kyoto: ¥10,990 (126mins, 380km)
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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 > Tokyo: ¥13,950 (194mins, 556km)
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Tokyo > Otsuki: ¥2,860 (85mins, 87km)
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Otsuki > Tokyo: ¥2,860 (76mins, 87km)
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Tokyo > Odawara: ¥3,840 (35mins, 83km)
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Odawara > Osaka: ¥12,070 (190mins, 472km)
JR ticket cost: ¥59,440 for 12 legs
As you can see you'll make a small saving with the 21 day JR Pass over this period. In addition to this saving you have the flexibility to add on further daytrips for free (more below). Also, you can make good use of the JR Pass on all JR lines within Tokyo while you are there. As the price of the 21 day pass is less than that of individual tickets, and you get 21 days of complete JR flexibility, I recommend the 21 day pass option for your long distance travel.
Please note that for Mt Fuji, I have assumed you will visit Kawaguchiko - the JR Pass will take you as far as Otsuki. From here you need to use the non-JR Fujikyu lines up to Kawaguchiko. Also, for Hakone the JR Pass will take you as far as Odawara. From here you need to use the non-JR Odakyu lines up to Hakone. I recommend the Hakone Free Pass for this.
As ideas for other locations that are not too far off your current itinerary, the majority of which you can get to using the JR Pass, I recommend:
- Naoshima
- Kurashiki
- Kinosaki Onsen
- Kanazawa
- Takayama
- Kumano
- Ise (Ise Jingu in partigular)
- Hakone
- Nikko
Hope this helps!