Try some of the beaches south of Lisbon. Cross the bridge (or take the cacilheiro) and go to the Costa da Caparica beach. It is a sandy beach extending for kms. It is divided into several concessions every 500 mts (+/-) most with their restaurant/bar. Try the ones farthest from the centre (Rei, Rainha, Riviera). If you dont have a car, get the bus to Costa da Caparica and then the mini/beach train to these beaches. You can also try some beaches further afield like Sesimbra, Praia do Meco e Arrabida / All only an half an hour from Lisbon by car. All these beaches are less touristic than Cascais for example but their sand quality is much better, you may find some secluded beach (ask the locals), you can eat at more reasonable prices on the beach and you can meet the real locals. One hour away and you can go to Troia by taking the ferry from Setubal another great white sandy beach.