There is a 14 day (and 21 day) as well.

You should check the price for tickets on the first two and last two days of your trip. If one of the amounts is less than the extra charge for the 14 day pass, then you should just get the 7 day pass and pay for two days worth of tickets individually. My guess would be that the Shinkansen from Hiroshima to Tokyo and then transportation from Tokyo to Narita is your single biggest expense, so you definitely want to use the pass that day. Check the cost of getting to Hakone and Takayama versus the extra cost of the 14 day pass.

Be aware that the Shinkansen does not go to the airport. If you are coming from Hiroshima, you will need to change at Tokyo Station (and earlier at Osaka Station, but that might be just across the platform). There is a special express to the airport from Tokyo. Reserve that in advance because it can sell out. I'd suggest booking your tickets from Hiroshima all the way to the airport for your final day when you redeem your pass.

Have fun!

In your situation a 14 day JR Pass might be about the same as a 7 day Pass and buying the extra tickets separately. You can go to hyperdia.com and figure out in detail - please make sure you use the total fare figure which includes the fare and seat fee.
Another possibility is using a 7 Day JR Pass for the first seven days and then flying back from Hiroshima to Narita. ANA has two flights a day and if you buy far enough in advance the price can be about 17000 JPY or $218 US which is almost the same as the difference between the cost of the 7 and 14 day JR Passes. Possibly you could do this on a special domestic ticket when you fly internationally for less.
The only cheaper way to travel is by bus - you can go to japan-guide.com to look up your destinations and see the different ways of accessing them.
Sounds like a great trip!

Is this itinerary unchangeable? Especially the last day with the long transit on the train and then on the plane back to your home? Are you staying in a ryokan in Hakone? What time does you plane arrive on your first day and what time does it leave on your last day? Sorry for all the questions but need to know so I can try and give you some options.

Aloha!

arrival/departure times for Narita and what airline(s) are you using for your international travel? A one-way fare in Japan could be as low as 10,000 yen depending on the airline you use? Did you purchase your tickets with money or is it a frequent flyer award? Do you have any frequent flyer miles? Only 6,000 United miles would get you a free one-way ticket from Hiroshima to Tokyo.

I think this itinerary might work better in reverse.

Sorry for taking so long to thank you all for your kind advice which is most helpful.
I have checked the individual prices for train fares and it works out best to buy the 14 day pass after all.

I will also follow your advice about seat reservations which is a very good idea.

Mrwunrfl asked me re flight times and I have just realised that the flight arriving at Narita from New Zealand which is an Air New Zealand flight does not arrive until 16.25 if on time.

I had mistakenly thought I was arriving in the morning. If I arrive at 16.25 on 4th January could I still get to my first stop over which is at a Ryokan in Gora/Kowakudani near Hakone?Or is this expecting too much in the winter and not being familiar with the country or able to speak Japanese? I would welcome any comments.

I am not a frequent flyer so have no air miles. Also I am departing Narita at 12noon on 14th Jan flying out with Virgin Airline. I will pend the night previous close to Narita Airport so no worries there.

Thanks again to everyone who took trouble to reply to me.

It's a 3 1/2 to 4 hour trip from Narita to Gora - you can look on hyperdia.com - there are a few changes - you obviously won't get there in time for dinner and there might not be much open at that time - haven't been to Gora myself.....there might be a direct bus - you can check into that but it would be a long ride....seems like you are better off staying one night in Tokyo...

Jo, others have touched on this possibility but it's worth further exploration. Since you arrive on a Star Alliance flight (Air NZ) you are eligible to purchase an ANA Japan Air Pass. That would let you buy a ticket from Hiroshima to Narita for ¥10,000 and you could get to Narita at 9:25 AM on the day of your departure. No need to overnight near the airport and you could buy a 7-day rail pass.
Details at http://www.ana.co.jp/wws/us/e/wws_common/fare/special/airpass.html

I just checked the fare for Hiroshima to Narita on ANA for a day in January (the 8th). The fare is 10,447 JPY. Depart 14:25, arrive 15:55. Add 1300 JPY for the bus from Hiroshima to the airport. Spend the night at Narita and fly the next day.

The train trip from Hiroshima, using a JR Pass, would be over 6 hours and involve a change of shinkansen trains at Shin Osaka (or other) and a change from the shinkansen to the Narita Express at Tokyo or Shinagawa.

Thanks again to you all for the further information you have taken so much trouble to get for me. I have lots of food for thought and think I will need to cancel the Ryokan in Gora as no point going there and missing out on the great food they serve at dinner if I cannot get there until very late.
Again a big thank you for all advice received

I was also going to suggest the 14 day pass, or even consider flying one of the low cost airlines from Hiroshima back to Narita. Also, when you take the shinkansen from Narita to Odawara (on your way to Hakone), change trains at Shinagawa station, NOT Tokyo station. It's a maze (and a nightmare to navigate). Even if you've been there before, Shinagawa is smaller and easier to change at, and you just go up and down escalators basically as the Narita Express platform is closest to the shinkansen platforms. Same thing if you take the shinkansen back to Tokyo and transfer to the Narita Express, DO NOT change at Tokyo station. Change at Shinagawa.

Maybe you could save yourself some money by buying a JR East or JR Kanto pass (depending on which works) for the first two days and then a 7-day JR pass.

The nice thing about the JR Kanto and JR East pass is that they cover the trip from Narita airport. The regular Japanrail pass does not cover the N'Ex. The Kanto pass is 80000Y for 3 days of travel. I haven't checked carefully but it might work for you if either pass gets you to Takayama. It will apparently get you to Hakone.
http://www.japan-rail-pass.com/japan-by-rail/travel-tips/jr-kanto-area-pass

I always prefer trains to flying because you have to factor in things like weather and getting from airport to city centers.

I have not done the research to see if the JR Kanto pass is a better deal...just offer it as something to look into. I have been to Japan three times but am not an expert.

Above poster is mistaken as the JR Pass definitely covers the Narita Express....

I have cancelled staying in Gora near Hakone as thanks to your advice I know I would be too late arriving there on my first day and have booked a hotel near the Shinjuku station in Tokyo for my first night.

i will then take the train to go to Takayama on day 2. using a 14 day JR rail pass.
Can anyone advise me about making this part of the journey on the 5th January and suitable train departure times as I want to leave Tokyo Shinjuku soon after 12 noon and where must I change trains? I want to be in Takayama in time for an evening meal at the hotel

When I come to make the final train journey from Hiroshima to Narita I will certainly follow the advice given to change at Shinagawa instead of Shinujuku station. Can you advise is good food available on the long distance trains?

Thank you for all advice received.Jo

All of the train information you need is easily available on www.hyperdia.com as has been advised in previous posts -- please take the time to use this invaluable resource.

As for food, you can often get terrific food in train stations rather than on the trains themselves. The best options are usually the bento boxes, which you can take on the train.

http://www.hyperdia.com/cgi/en/search.html?dep_node=SHINJUKU(JR)&arv_node=TAKAYAMA&via_node01=&via_node02=&via_node03=&year=2013&month=01&day=05&hour=12&minute=00&search_type=0&search_way=&transtime=undefined&sort=0&max_route=5&airplane=off&ship=off&sprnozomi=off&lmlimit=null&search_target=route&facility=reserved&sum_target=7

Sounds like you are a little confused. Tokyo Station and Shinjuku Station although both in Tokyo are two seperate stations in two different parts of Tokyo. You want to avoid Tokyo Station and use Shinagawa Station as a transfer point back to Narita transferring from the shinkansen(bullet train) to the NEX (Airport Express)Train.

Aloha!