I'm not sure if you want a JR Pass (Japan Rail Pass). It's not worth it if you're only going to one place, namely Kyoto. it costs ¥28,700 for a 7 day pass. Shinjuku-Kyoto round trip on Nozomi is ¥25,410. If you're going to take the Narita Express to and from Narita, then the JR Pass might be worth it.
Assuming you are NOT getting the JR pass:
Shinjuku-Hakone purchase Odakyu Free Pass. Since you'll be only using the Free Pass back to Odawara on your way to Kyoto, you can purchase a regular train ticket to Odawara from Shinjuku (¥850 on express; add extra to take reserved Romance Car), then get the Free Pass which covers the train ticket from Odawara to the Hakone "Loop." (¥3,900)
After Hakone, go to Odawara, and catch the Hikari Shinkansen to Kyoto. (will be cheaper than taking the Nozomi.)
Kyoto to Tokyo, get Nozomi Shinkansen.
Train schedules http://www.jorudan.co.jp/english/norikae/
Edited: 4:20 am, October 13, 2013