The fastest way to Kamakura Station is by JR Yokosuka Line from Tokyo Station (one hour, ¥890) and Yokohama (25 minutes, ¥330). Also the JR Shonan-Shinjuku line from Shinjuku Station platform 1 or 2 (one hour, ¥890).

The JR Kamakura-Enoshima Pass gets you a round trip with unlimited use of JR, Enoden and Shonan Monorail lines. You can buy the ticket at Ofuna, Fujisawa, Kamakura or Kita-Kamakura Station.

An alternative is to take the private Odakyu line from Shinjuku to Fujisawa, then change onto the rattling old Enoden (江ノ電) half-train/half-streetcar line that terminates in Kamakura. The longer (about 90-minute) travel time is compensated for by views of Enoshima island and the Shonan coast.

The Enoshima-Kamakura Free Pass will get you a roundtrip from Shinjuku and unlimited use of the Enoden line for one day.