All year around people visit Kamakura for sightseeing. In spring they come for cherry blossoms. In autumn they come for color change. Japanese-maple, gingko trees, Hazenoki (a family of Lacquer tree) and a few other trees turn red, yellow and bright brown in hill- sides and in the grounds of temples and shrines.
Hill side hiking in autumn is a special experience. The place I recommend is Lion-dance valley. Until a few years ago this place was known soley for the local people, but it has become more popular recently. Japan National Tourism Organization featured this place in 2012. Please click JNTO web sight to see how beautiful it is
I go there every year. Last year the best timing was the 1st week of Dec. , but it varies year by year. It takes 1 hour from Kamakura station. Along the way there are many famus temples and shrines, therefore you can enjoy both hiking and historical spots. You need a pair of walking shoes so as not to stumble. When it rains on the tour day or on the previous day, it is very slippery.
More Kamakura information for you!! Some temples in Kamakura hold light-up events at night. For example Hasedera Temple holds light-up at night from end of Nov to begining of Dec. They have a website in English.