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.