If I go to Kamakura / Route Plan

I made a route plan for your reference! If you can depart in the morning, it's perfect because the early bird gets warm! But the commuter rush in Tokyo is terrible, so I recommend arriving at Tokyo Station when the rush is over. 10:00 is perfect ( I hope so).  
I have had many short trips to Kamakura, and here is my favorite course. Let's get started!

Take a Taxi to Tokyo Station / "Marunouchi Chuo-Guchi" is the best gate to go to Kamakura. 
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TOKYO STATION - Sobu-Yokosuka Line
* It's a bit complicated to get to the Sobu-Yokosuka Line. I recommend asking the train staffs how to get to the right platform. 
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"Green Car"

Sobu-Yokosuka Line has regular and upgraded seats - The upgraded seats are in a separated car called "Green Car" (see example above, #4 car is Green Car in this case). If you want to try Green Car, just find the "four green leaves" sign and get on it without reservation. It is a first-come, first-served basis and you need to pay an additional fee (around $10) on the train. A crew person will come to you and ask about your final destination.
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KITA-KAMAKURA STATION
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Lunch or Coffee Break: my favorite places nearby Kita-Kamakura Station
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ENGAKU-JI
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MEIGETSU-IN
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KENCHO-JI
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TSURUGAOKA-HACHIMANGU 
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KAMAKURABORI SANSUI-DO  Kamakura-Bori (Curving)
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KOMACHI-DORI  Walk around to KAMAKURA STATION
* You can see various shops in Komachi-Dori. Food, souvenirs, etc.