Whether you are long-term resident, fluent in Japanese, know your way around town, or are a short-term visitor, can't speak or read a word of Japanese, and have no idea where you are going in Kyoto - you will need a toilet at some point.
The best options are convenience stores, department stores, restaurants, and inside train stations (that is, after you have paid and entered the station).
When those options are not readily available - unusual as convenience stores are everywhere - here is a map that notes public, free, and sometimes wheelchair-accessible toilets. (For the final type, your best bet is department stores.)
Kyoto Public Toilet Map
View Public Toilets Kyoto in a larger map
Tags Japan Touring Kyoto Cycle Japanese