There are several beaches local to Tavira.  If you are not driving then Ilha de Tavira is your best bet.  This is on an island half a kilometre from Tavira, reached by ferry for €1 (70p) return. From the centre of town the tourist train will take you to the ferry.

If you are driving then the local beaches at Cabanas, Monta Rota, Praia Verde and Santa Luzia are all amazing & well worth a visit.