The river flows down through Newlands and Rondebosch to meet up with the Black River, which then flows through Paarden Island (an industrial area on the outskirts of the city), finally ending up in Table Bay. I managed to follow the river using Wikimapia from where it joins with the Black River and then up towards its source.
In searching for information about the river I discovered a group called "Friends of the Liesbeek" - a privately run organisation involved in conservation of the river and the animals that live in it. I believe that the group raises funds and actually employs people to clean away pollution.