Travelling 2Km to the West from the city you will find Santa Luzia, very much like Cabanas de Tavira, it's origins are fishermen, and it's known nowadays as "Capital do Polvo" in English "Octopus Capital" which is a local speciality, featuring many ways of cooking and preparing octopus.
From Santa Luzia you can catch the mini-train and visit Barril beach, which is an extension of Tavira island 3Km East.