Madeira’s airport is in the East of the island so on your arrival in Madeira for your self catering holiday you will get a feel for this part of the island. The coastline further past the airport in the most Easterly part of the island is interesting and attractive and takes the form of an interesting thin coastline which stretches out to sea. At Prainha in the very east there is an ecological park and you can enjoy coastal walks. Take great care when walking here though. It is recommended that you wear proper walking boots and take a walking pole. This part of the island is no place for children. There are amazing coastal views but a shocking lack of barriers making it a treacherous place for children and even adults must keep their wits about them and take great care.
The eastern part of the island is attractive enough but lacks the attractions of other parts of Madeira such as Funchal. If you are looking to a holiday in a part of Madeira though which is reasonably quiet you may be attracted to the east of Madeira.