A twenty minute walk away from Kita-Kamakura Station lays perhaps one of the most interesting yet, underrated hikes that this city has to offer. Known as the Rokkoku-Kenzan Hiking Course, this walk passes through several small tunnels, a quiet residential area, then traverses up to the top of Mount Rokkoku Kensan. Standing at 300 meters high, the top of this hill offers some fine views of Mt. Fuji (mainly in the winter) as well as the bay below.
Although there is little information available in English, with a little perseverance you can follow this interesting course by downloading a walking map at this site.