
If you just want to go for a swim, Ria Formosa lagoons offer clean quite and warm water at high tide just 5 minutes away from Casa Flor de Sal.
If you want the real beach experience, then there are plenty of choices at hand:

The beaches closest to Casa Flor de Sal are in Fuseta and can be reached walking or biking (3.5km) on the Ecovia (natural path) along the nature reserve. Alternatively one can drive there.
Fuseta has two beaches for you to choose from. The first is a small beach on the lagoon in the town itself which is quite protected and has cafes and ice cream sale open virtually all year. Families with small children will appreciate it as being in the lagoon it is wave free and very safe. The water is also always a little warmer than the beaches facing the open sea. However, it is somewhat muddy at the lowest tide (The lagoons have a muddy bottom and this is where seafood is picked & farmed).

You can also hire a boat taxi from Fuseta to bring you to your "own" beach, as these people did.

Armona has bars, restaurants, and multiple beach choices: you can swim on the lagoon shore by the pier or explore the lagoon shore around the edge of the village out to the Atlantic beach. Both these areas are quite protected and shallow and one can spend quite sometime playing in the water and observing the massive amounts of live shellfish and small fish that sometimes even come and peck on your feet and legs! Alternatively, you can head straight for the ocean beach. To the left, Armona beach runs on for miles until you reach Fuseta’s Atlantic beach. Everywhere in between is essentially empty and it is all beautiful.
You can spend a day at Armona beach by asking us to take you there kayaking or you can catch a ferry from Olhão. The ferry goes from the pier at the eastern end of the waterside gardens in Olhão. It has a fixed timetable and takes about 15 minutes to get across.

Barril beach is on Tavira Island. This island is 18 km long and Barril is about in the middle of it. Walk left, to the east, and you will come to St.Luzia's beach at Terra Estreita, and then eventually to Tavira beach right at the end of the island. Walk right, to the west, and after about 1.5h you will come to the tip of the island at Pinheiro. At this point, you would be able to see Fuseta island. Barril is a BIG beach.

To reach Barril from Casa Flor de Sal, you should take the N125 in the direction of Tavira. A few km after you have past the village Luz de Tavira, you should see signs on the right for Barril and Pedras d´el Rei. Follow these, and after passing the holiday village you find somewhere to park, cross the foot brigde and either walk or take the little train to the beach.

You can also take the ferry to Culatra or Farol, this is a bit longer and as the ferry does not run quite as often it is best to check the timetable first (or plan for a taxi boat). Culatra has a little village with both a church and restaurants and long, uncrowded beaches, it is really getting away from it all.
Other beaches:
Praia de Tavira, Manta Routa, Altura and Praia Verde are other nice beaches all within 30 minutes drive.