Travel down to the peninsula is easy.
From Tokyo station, you can get to Atami on the Shinkansen for a 40 minute journey. Alternatively, the Tokkaido line takes two hours( and costs about ¥2000).
If you are travelling as far as Shimoda, it is worth the few extra thousand yen and making that journey shorter.
(Tokyo - Atami on the shinkansen = (approx) ¥4000, Atami to Izukyushimoda = ¥1900)
There is also the special Odoriko train from Shinjuku (which also stops in Atami) which will take you direct to Shimoda in just under three hours, setting you back just over ¥6000. (¥4000 from Atami)
The trains commemorate Matthew Perry's landing with his 'Black Ships' back in 1853. A novelty we were happy to experience!