Free public places can be found on this map of the city of Düsseldorf

https://www.duesseldorf.de/umweltamt/umwelt-und-verbraucherthemen-von-a-z/klimaschutz/weitere-themen/stadtklima/karte-der-kuehlen-orte

A selection of drinking water dispensers is also given in the list below (PDF).

All information subject to change.