Madeira is riddled with water courses called levadas. In many cases there are paths beside them, hwich provide for magnificent walking. Don't get the idea that it's all easy. it varies in difficulty from very simple - almost level broad paths to very demanding mountainous walks.

Public transport is not very good for much levada walking but there are several travel agencies that arrange levada walks and these, of course, provide transport. There's a good Cicerone Guide.