Hi there,
Looks like a great trip!
To understand if a 14 day pass (¥45,100) is worthwhile we need to do a calculation of the normal JR ticket costs of your trip. Lets take a look at your approximate projected costs:
- Narita airport terminal 1 > Kyoto: ¥15930, (238mins, 592km)
- Kyoto > Nara: ¥690, (45mins, 41km)
- Nara > Kyoto: ¥690, (44mins, 41km)
- Kyoto > Kobe(hyogo): ¥1050, (56mins, 75km)
- Kobe(hyogo) > Kyoto: ¥1050, (55mins, 75km)
- Kyoto > Himeji: ¥5130, (68mins, 130km)
- Himeji > Kyoto: ¥2210, (91mins, 130km)
- Kyoto > Toba: ¥8230, (177mins, 270km)
- Toba > Kyoto: ¥8230, (161mins, 270km)
- Kyoto > Tokyo: ¥13220, (161mins, 513km)
- Tokyo > Kamakura: ¥1900, (48mins, 51km)
- Kamakura > Tokyo: ¥890, (58mins, 53km)
- Tokyo > Odawara: ¥3640, (35mins, 83km)
- Odawara > Tokyo: ¥1450, (36mins, 83km)
- Tokyo > Otsuki: ¥2860, (84mins, 87km)
- Otsuki > Tokyo: ¥1450, (100mins, 87km)
- Tokyo > Nikko: ¥5430, (121mins, 150km)
- Nikko > Narita airport terminal 1: ¥8460, (209mins, 229km)
TOTAL: ¥82,510 for 16 legs
As you can see, a 14 day pass will get you minimum savings of ¥37,410. You also have flexibility to change your plans as you travel. For these reasons I can recommend the 14 day pass for your itinerary.
I think your itinerary spacing looks busy, but good if you're up for it! I recommend you travel to either Hakone or MtFuji/Kawaguchiko (rather than both), and maybe give Hakone an overnight stay in an onsen if you do go there.
Please note that for Hakone the Rail Pass will get you as far as Odawara. From here you should use the non-JR Odakyu lines to get up to Hakone. I recommend the Hakone Free Pass if you visit.
Hope this helps!