Hi there!
Here are the relative costs of the 14 & 21 day passes:
14 & 21 day rail pass costs
- 14 day: ¥45,100 / ¥3221 per day
- 21 day: ¥57,700 / ¥2747 per day (+¥12,600 over 14 day pass)
You'll need to spend more than this on JR tickets for them to be worthwhile. Lets first take a look at your costs, then consider your daughters case last.
Parent plans
- Narita airport terminal 1 > Tokyo: ¥2740, (62mins, 79km)
- Tokyo > Hiroshima: ¥17850, (295mins, 894km)
- Hiroshima > Kyoto: ¥10590, (126mins, 380km)
- Kyoto > Sendai(miyagi/jr): ¥20680, (304mins, 865km)
- Sendai(miyagi/jr) > Ishinomaki: ¥3380, (123mins, 80km)
- Ishinomaki > Sendai airport: ¥1850, (139mins, 88km)
TOTAL: ¥57090 for 6 legs
As you can see from your costings, you will save money on both types of passes, but stand to make much more of a saving using a 14 day pass (¥11,990) provided you don't intend to do much JR travel while in Tokyo. I think in your case I would recommend using a 14 day rail pass and purchase individual tickets as needed for your trip into and around Tokyo. For Tokyo from Narita I recommend one of two options:
-
2 day metro pass with the Keisei Skyliner to get you into Tokyo from Narita inclusive of 2 days unlimited travel on the Tokyo Metro.
- [Narita Express + Suica metro prepaid card] deal. This is similar in terms of cost, but rather than 2 days of full metro cover, it gives you ¥1500 of Metro and JR travel which can be used however you like and offers travel into Tokyo on the Narita Express rather than the Keisei Skyline train. You can also use the Suica card to purchase food from convenience stores.
Daughter plans
Assuming your daughter is doing an identical trip to yourselves but with an extra week bolted onto the end, lets take a look at her ticket costs:
- Narita airport terminal 1 > Tokyo: ¥2740, (62mins, 79km)
- Tokyo > Hiroshima: ¥17850, (295mins, 894km)
- Hiroshima > Kyoto: ¥10590, (126mins, 380km)
- Kyoto > Sendai(miyagi/jr): ¥20680, (304mins, 865km)
- Sendai(miyagi/jr) > Ishinomaki: ¥3380, (123mins, 80km)
- Ishinomaki > Tokyo: ¥11440, (235mins, 422km)
- Tokyo > Narita airport terminal 1: ¥2740, (58mins, 79km)
TOTAL: ¥69420 for 7 legs
The return from Sendai to Tokyo + the trip to Narita will cost ¥14,180 and so will cost more in plain ticket costs than the ¥12,600 upgrade from 14 day to 21 day pass. In total her savings will be ¥11,720 based on the above itinerary and 21 day pass. With a 14 day pass and individual tickets back to Tokyo her savings will be ¥10,140. Based on this I recommend your daughter purchases a 21 day rail pass for maximum savings and flexibility during her final week in Japan.
I hope this helps - please let me know if you'd like me to clarify anything!