If you want to see Kyoto without using public transportation, you may want to rent a bicycle.
Tamakikat and I saw these bicycles parked near Heian Shrine. They are from Kyoto Eco Trip. The prices on their site seemed pretty reasonable, plus there is a cool gadget to hold your water.
The link above is in Japanese only (sorry!)
Kyoto Eco Trip
(near JR Kyoto station)