The Arashiyama District is an easy train ride from Kyoto Station. The main street is kinda touristy but should not be overlooked if for no other reason than the availability of green tea, black sesame and yuba tofu soft serve ice cream cones.
A pleasant walk or bike ride through the district will leads to multiple shrines, the Kameyama-koen monkey park, and the river where you can rent a boat and do some rowing.
Don't miss the tranquilic bamboo grove. Walking through the towering green stalks is slightly surreal.