Just outside of Tavira is a 11 km long Island named Ilha de Tavira.
Ilha de Tavira has some of the Algarve's best beaches, and can be accessed either by ferry or via the footbridge from Santa Luzia.
In summer period, ferries depart both from Tavira and from 4 aguas (The 4 water).
From 4 Aguas it takes about 5 min. while it takes 15 min. from Tavira, but it is a very beautiful trip out through the river Gila and delta so.
You can also use the bridge at Santa Luzia and the associated small railtrack.
The beach itself is one of the most beautiful in the Algarve, there is plenty of life in the East End where people bathe, play ball, take sun mm. while being quieter the further west you go.
Photos from Ilha da Tavira: Ilha da Tavira