Hi there,
A 7 day rail pass is ¥28,300 and 14 day is ¥45,100. You'll need to be spending more than each of these amounts for the respecive rail passes to be cost effective. Lets take a look at the real ticket costs of your journey you will use JR for:
- Narita airport terminal 1 > Nikko: ¥8060, (186mins, 229km)
- Nikko > Kanazawa: ¥15360, (313mins, 550km)
- Kanazawa > Kyoto: ¥6510, (126mins, 224km)
- Kyoto > Hiroshima: ¥10590, (112mins, 380km)
- Hiroshima > Nara: ¥11060, (165mins, 393km)
- Nara > Shinmatsuda: ¥12390, (259mins, 488km)
- Shinmatsuda > Tokyo: ¥1610, (118mins, 82km)
- Tokyo > Narita airport terminal 1: ¥2740, (58mins, 79km)
TOTAL: ¥68320 for 8 legs
As you can see a 14 day rail pass will give you great savings of ¥23,220 so I can certainly recommend this choice as the simplest of your options that will save money.
As to whether you'll be better off with a 7 day pass + standard JR tickets, we need to see if there's any way you can spend less than the difference between 7 and 14 day jrpass (¥16,800) on normal JR tickets if using a 7 day pass. Looking at the cost break down, if you did start a 7 day rail pass on day 3 until 9, the other JR tickets costs you list would come to ¥12,410, which is cheaper than going for the upgrade to 14 days. This means you could save a further ¥4390 by using a 7 day pass + standard JR tickets over going for a 14 day pass. Of course, there's always a tradeoff, and in exchange for the extra ¥4390 savings, you loose the flexibility and use of the 14 day rail pass when your 7 day pass is not active. Ultimately your choice here will rest on how definite your plans are, but I think if I was in your position I may go for the 14 day pass simply to keep my options open.
Hope this helps!
