Hello lydia@ , you can go to the Rathaus in Köln where you want to live and request for Wohnberechtigungsschein and from you will be giving a list of social apartments that are near to rent in a cheapest prices because according to my research, I find out that Köln is big, so I can't send you a link for social apartments but you can first visit the actual place in Köln you wish to stay to obtain the Wohnberechtigungsschein and you will giving additional list of cheap social apartments. Thanks