Hi there,
This is a 15 day trip, so we'll leave one of your Tokyo>Narita legs out of our calculations as they won't fit into a 14 day rail pass. That being said, here is the approximate breakdown of your travel costs:
- Narita airport terminal 1 > Tokyo: ¥3140, (62mins, 79km)
- Tokyo > Kyoto: ¥13420, (165mins, 513km)
- Kyoto > Osaka: ¥540, (28mins, 42km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Nara: ¥690, (49mins, 41km)
- Nara > Kyoto: ¥690, (46mins, 41km)
- Kyoto > Nagano: ¥10930, (237mins, 398km)
- Nagano > Tokyo: ¥8170, (106mins, 222km)
TOTAL: ¥38120 for 8 legs
Certainly, it doesn't seem worth buying a 14 day rail pass (¥45,100) to cover a lot of your trip, mainly because you will be spending a big portion on the ski slopes - lucky you!.
The only alternative I can think of here is a 7 day rail pass from the 23rd to the 29th:
- Tokyo > Kyoto: ¥13420, (165mins, 513km)
- Kyoto > Osaka: ¥540, (28mins, 42km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Nara: ¥690, (49mins, 41km)
- Nara > Kyoto: ¥690, (46mins, 41km)
- Kyoto > Nagano: ¥10930, (237mins, 398km)
TOTAL: ¥26810 for 6 legs
As you can see, from the legs you have mentioned here, it still will be slightly cheaper to buy separate tickets as you go than a 7 day JR Pass at ¥28300.
However, if you were to mix in some more travel on the 23rd and 24th (eg, Nikko, or trips on the JR lines around Tokyo as you explore the city), you could easily push your travel costs over the ¥28,300 barrier where a 7 day JR Pass becomes cost effective. With a Japan Rail Pass, you also have the added benefit of not worrying about buying tickets before travel. I think this convenience factor alone makes using a rail pass worthwhile, but in the end it's down to personal choice - On price alone, it's a very close run thing!
For more train times and prices, you can use the travel planning website, www.hyperdia.com. You can also see our online guide for how to use Hyperdia for JR Pass holders.
Hope this helps!