As a 7 day rail pass is ¥28,300, you'll need to spend more than that in individual tickets for a rail pass to be worth it.
Lets take a look at the ticket costs for your itinerary within the first 7 days:
- Kansai airport > Shinjuku(jr): ¥15330, (287mins, 617km)
- Shinjuku(jr) > Maihama: ¥380, (46mins, 23km)
- Maihama > Shinjuku(jr): ¥380, (46mins, 23km)
- Shinjuku(jr) > Odawara: ¥3440, (58mins, 87km) (this is for Hakone)
- Odawara > Shinjuku(jr): ¥1450, (60mins, 87km)
- Shinjuku(jr) > Osaka: ¥13550, (214mins, 560km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Osaka: ¥540, (28mins, 42km)
TOTAL: ¥35610 for 8 legs
Based on these ticket costs, a 7 day rail pass will give you a saving of ¥7310 over tickets, and you'll have a lot of flexibility to visit other places, such as Nikko, while you are in Tokyo.
Although I use the prices for Hakone for your Mt Fuji leg, you also have the choice of going to Kawaguchiko if you want to get a bit closer, or intend to climb (only possible during the summer).
Here is a sample itinerary from Kansai Airport to Shinjuku. You can look up train timetables and costs at the Hyperdia travel planning website and learn how to use Hyperdia for Japan Rail Pass holders through our video blog.
Hope this helps!