tokyo-hakone-kyoto-osaka-tokyo

Hello, I am finding figuring out travel within Japan rather confusing, and don't know whether I should purchase a 7 day pass to use from March 14th - 20th (covering from Hakone - Kyoto - Osaka - Tokyo) or a 14 day pass (to also cover Airport - Tokyo (and travel around Tokyo for 6 days) - Hakone - from March 7th to 20th). Some help would be greatly appreciated! (As I also dont even know if JR lines travel to Hakone?)

I arrive on the 7th March in Tokyo then this is my itinerary:

March 7th - 12th: travel within Tokyo (around Ueno, Shinjuku, Harajuku etc)

March 13th: travel from Tokyo to Hakone

March 14th: Hakone - Kyoto

March 14th - 17th: (visit Tofuku-ji Temple, Arashiyama bamboo forest, Tenryu-ji Temple, Inara Shrine), day trip to Nara

March 17th: Kyoto - Osaka

March 17th - 19th: travel around Osaka and day trip to Hiroshima

March 19th: overnight train to Tokyo

March 23rd: leave back to New Zealand.

Thank you :)

March 7th - 12th: travel within Tokyo (around Ueno, Shinjuku, Harajuku etc)
1) March 7 - Pls buy the N'ex Tijti Direct Ticket at Narita Airport (one way 1,500 yen) http://www.jreast.co.jp/e/pass/nex_oneway.html


March 13th: travel from Tokyo to Hakone
--- Please buy Hakone Free Pass from Shinjuku to Hakone http://www.japan-guide.com/e/e2358_008.html

March 14th: Hakone - Kyoto
---- From March 14 to March 20, Pls use JR rail pass 7 days

March 14th - 17th: (visit Tofuku-ji Temple, Arashiyama bamboo forest, Tenryu-ji Temple, Inara Shrine), day trip to Nara

March 17th: Kyoto - Osaka

March 17th - 19th: travel around Osaka and day trip to Hiroshima

March 19th: overnight train to Tokyo

March 23rd: leave back to New Zealand.
--- Please buy JR Ticket or Airport Limousine bus ticket.

Thank you!! Is there a JR train straight from Hakone to Kyoto? Or do I have to catch the train back to shinjuku on the Hakone pass first?

You can take the train from JR Odawara station. In Hakone, You can use Hakone Free Pass to Odawara Station from Hakone area. Have a nice trip.