Shinjuku to Kamakura and endoshima, recommended travel route:-
Using JR line or
Odakyu line.
Any free pass worth it?
I bought Enoshima-Kamakura Freepass from Odakyu Sightseeing Service Centre located at Shinjuku Station during my visit in last December. The freepass includes a round trip ticket from Shinjuku to Fujisawa (We topped up the limited express surcharge to ride on Odakyu Romancecar and traveled to Katase-Enoshima instead), unlimited rides on Enoden line (Enoshima electric railway) and discounts on participating facilities such as Enoshima ESCAR, aquarium, lighthouse observatory tower etc. For more info on this freepass, refer to odakyu website.
I read that you wish to ride the Shonan monorail, for that you have to ride from Ofuna station which is about 51 mins from Shinjuku station. You may get the Kamakura-Enoshima Pass (JR) which includes unlimited rides on Kamakura-Enoshima Shonan Monorail, JR Line between Fujisawa Station, Ofuna Station and Kamakura Station, and Enoshima Electric Railway. You can buy this pass at JR Ofuna, Fujisawa, Kamakura and Kita Kamakura Stations only.