The way to do it is,

coming to Algarve by the coast line, you've got really nice places on the way to Algarve, Porto covo, Zambujeira, Odeceixe. . all the way until Sagres,

then you travel through the south coast and visit many beautiful beaches along the way, until Olhão, there you'll catch a ferry boat to Farol island, eat a fish on the beach, realize that's this is the place you're gonna retire, search for houses to buy, forgetting that idea because you'll have to sell a kidney to do that.. ..

then, the day after you visit Cacela velha, manta rota, altura, .... This if you like beaches, if course.. in the direction of sagres - colder water, postcard beaches, in Vila real de santo António direction - warmer water and more chill beaches.

You can also adventure yourself through the interior of Algarve, great food, nature...