Kamakura is one hour away from Tokyo, on the Yokosuka line.
You can enjoy the mountain, the beach and walk to Enoshima. Temples, with the great Buddha statue is a must while quite touristic. It is impressive though. There are other beautiful temples, around Hase and Kita Kamakura. In automn, there is a festival of Yabusame: archery on horse.
There are a lot of nice places to eat, have a cup of coffee or tea that will send you back in early 19th century.