Hi Wendy,
The JR Pass is valid on the Miyajima ferry so you should have no problems there. However, as the Tokyo subway (known as "Tokyo Metro") is not operated by JR, you will be unable to use the JR Pass on it. With a JR Pass you are able to use JR's network of trains that cover much of Tokyo (here's a map of JR lines in Tokyo), but these are not quite as convenient as the Metro and you will inevitably purchase some Metro travel. Exactly how much Metro travel you'll need to buy depends on your destinations within Tokyo.
If you intend to do day trips outside Tokyo (to Nikko for example) during your initial 5 days, then I would recommend a 21 day pass. However if you intend to explore the city, I think I'd recommend:
- Purchase a Single [N'EX (narita express) ticket into Tokyo + Suica metro prepaid card bundle] on arrival at Narita. The Suica card is like an Oyster card on the London underground. This deal will basically give you ¥1500 worth of metro travel for free. You may need to top this up while you're in Tokyo, but it should get you off to a good start. You can learn more about the Suica card in our blog post on pre-paid travel cards in Tokyo.
- Purchase a 14 day Japan Rail Pass for use starting on your 4th day or for your trip out to Mt Fuji. This should cover you for travel all the way back to Narita airport on your final day.
As a final check, lets make sure you'll get good value from a 14 day pass. A 14 day rail pass is ¥45,100 so you'll need to spend at least that in tickets to make it worthwhile. Here's your itinerary from going to Mt Fuji (I have assumed Kawaguchiko for this - you'll be able to take JR as far as Otsuki, and then from there will need to use non-JR trains for the final leg to Kawaguchiko).
- Tokyo > Otsuki: ¥2860, (85mins, 87km)
- Otsuki > Takayama: ¥15460, (453mins, 578km)
- Takayama > Osaka: ¥10310, (220mins, 357km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Osaka: ¥1680, (27mins, 42km)
- Osaka > Nara: ¥780, (51mins, 48km)
- Nara > Osaka: ¥780, (55mins, 48km)
- Osaka > Hiroshima: ¥9950, (103mins, 345km)
- Hiroshima > Miyajimaguchi: ¥400, (26mins, 21km)
- Miyajimaguchi > Narita airport terminal 1: ¥20340, (408mins, 995km)
TOTAL: ¥63100 for 10 legs
As you can see you'll make good savings of ¥18,000 with a 14 day rail pass so I can certainly recommend this option.
By the way, as you mention you have 1 night unaccounted for towards the end of your trip, how about an overnight stay at Kinosaki Onsen hotspring bath town? It's around 3hrs from Osaka, but is a fantastic little town with many Onsen, a great atmosphere and routinely described as the best Onsen town in the area of Hyogo. Here's a good forum post with more, and you can also book many onsen online. Here's a good tripadvisor with people's opinion of the town to give you a flavour of what to expect.
Hope this helps!
