Hi there, for a 14 day pass to be worth it you have to aim to spend over ¥45,100 on individual rail tickets. Lets take a look at your itinerary:
- Narita airport terminal 1 > Tokyo: ¥2940, (62mins, 79km)
- Tokyo > Nikko: ¥5430, (121mins, 150km)
- Nikko > Tokyo: ¥5430, (117mins, 150km)
- Tokyo > Kyoto: ¥13220, (165mins, 513km)
- Kyoto > Hiroshima: ¥10790, (109mins, 380km)
- Hiroshima > Kyoto: ¥10790, (126mins, 380km)
- Kyoto > Kobe(hyogo): ¥1050, (56mins, 75km)
- Kobe(hyogo) > Kyoto: ¥1050, (55mins, 75km)
- Kyoto > Osaka: ¥540, (28mins, 42km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Tokyo: ¥13220, (161mins, 513km)
- Tokyo > Narita airport terminal 1: ¥2940, (58mins, 79km)
TOTAL: ¥67940 for 12 legs
I've not included travel around Tokyo in this calculation, but you could perhaps increase the total by around ¥1000 if you plan on using JR lines in Tokyo.
As you can see you are planning on at least ¥67,940 worth of travel on this trip, making a 14 day rail pass well worth it. In total a 14 day japan rail pass will give you a saving of around ¥20,000 per person. As the 14 day rail pass won't cover one of your Tokyo<>Narita legs, I recommend you activate your JR Pass on the second day in Japan (25th) that should cover you right up until you leave.
To get into Tokyo from Narita on arrival, you should purchase a [Narita Express & Suica prepaid metro card deal] for ¥3,500 when you get to Japan. This gives you the Narita Express to Tokyo trip (normally ¥2940), and also a Tokyo Metro travel card (suica type) precharged with ¥1500 (normally costs ¥2000). This combined offer will mean you make a good saving on travel inside Tokyo as the metro is sometimes the most convenient way to travel. Also, the prepaid card is really the most convenient way to use the metro system over standard metro tickets. With ¥1500 for metro travel and free JR travel you should be all set!
Hope this helps!