Kamakura is a very nice one hour day trip outside of Tokyo, and makes a nice part of a trip that otherwise keeps you in the urban sprawl of Tokyo. Kamakura is only an hour away by direct train, but gives you a chance to see a bit of the suburbs and a tiny flash of countryside, as well as many interesting temples and of course, the Great Buddha statue. The city was once the political and cultural capital of the Shogunate, from 1192 to 1333, so there is some history to absorb as well.
While not quite on par with beautiful Kyoto and stately Nara, Kamakura has at least a dollop of the Japan you have read about and seen in the movies. Read on.