Kamakura is an easy day trip from Tokyo. The JR Yokosuka Line runs direct from Tokyo Station and Shinjuku (via Shibuya) to Kamakura Station in about 55 minutes to one hour. The Japan Rail Pass covers this journey. Kita-Kamakura Station, one stop before Kamakura, is the best arrival point for the Zen temples at the north end of the city.
Alternatively, take the Odakyu Line from Shinjuku to Fujisawa, then connect to the Enoden line and ride it along the coast to Kamakura Station — a slower but scenically rewarding route. From Yokohama, the Yokosuka Line takes around 25 minutes.
Driving is possible but unnecessary and parking is scarce on busy weekends. The train is by far the better option.