!14 days jrr pass?

Hi there!

Looks like a great trip! You may want to consider Nikko, or an overnight stay at an onsen hotspring while in Hakone (or by visiting Kinosaki onsen while you are in the Osaka area), but in general I think you have a lot of interesting things to see.

To understand if a 14 day rail pass (¥45,100) is right for you we need to take a look at the ticket costs for your journey:

1. Tokyo > Nikko: ¥5430, (121mins, 150km)
2. Nikko > Tokyo: ¥5430, (117mins, 150km)
3. Tokyo > Kamakura: ¥1900, (48mins, 51km)
4. Kamakura > Tokyo: ¥890, (58mins, 53km)
5. Tokyo > Odawara: ¥3640, (35mins, 83km)
6. Odawara > Tokyo: ¥1450, (36mins, 83km)
7. Tokyo > Kyoto: ¥13220, (164mins, 513km)
8. Kyoto > Osaka: ¥540, (28mins, 42km)
9. Osaka > Kyoto: ¥540, (29mins, 42km)
10. Kyoto > Nara: ¥690, (45mins, 41km)
11. Nara > Kyoto: ¥690, (44mins, 41km)
12. Kyoto > Himeji: ¥5130, (68mins, 130km)
13. Himeji > Hiroshima: ¥8070, (60mins, 249km)
14. Hiroshima > Miyajimaguchi: ¥400, (26mins, 21km)
15. Miyajimaguchi > Tokyo: ¥18050, (331mins, 916km)

TOTAL: ¥66070 for 15 legs

As you can see you'll make minimum savings of ¥20,970 with a 14 day rail pass so I can certainly recommend you purchase it in your case. Please note that for Hakone the JR Pass will get you as far as Odawara. From here you will need to use non-JR Odakyu trains to get you up to the Hakone area. I recommend you try and do an overnight stay in Hakone, and purchase the Hakone Free Pass at Odawara for travel in this area.

Hope this helps!