We stayed at Four Seasons Vilamoura for a week - my goodness, was it 15 years ago now? Lovely place, at least then. One of our favorite vacations.
You'll love the town of Vilamoura, though Four Seasons is just far enough from the marina (which is the center of activities), that it's a bit of a walk, but short enough that it seems indulgent to drive. IIRC, there's a little tram that runs around that can take you there. Loved the marina -- lots of wonderful restaurants lining the large marina berthing multi-million dollar yachts. Many of the restaurants are very reasonably priced, though of course not all. My profile picture is from one of those restaurants. Again, one of our favorite vacations.
It's very easy to drive the entire Algarve and back in one day, though you may want to take more time to take in all the quaint towns. Our favorite was the town of Lagos. If you drive out to the end of the peninsula, to an area called Ponta da Piedade, there are stairs that you can take down the limestone cliffs to the rocky area at the bottom. There, you'll find (assuming it's the same as when we went) an area that fishermen take their boats to give water tours to tourists for a reasonable fee. Ours was both funny and irreverent -- some of the rock formations have very bawdy local names. Loved it.
Or, you can take commercial boat tours of the entire coast, much of which is interesting rock formations in the limestone cliffs. There are boat tours leaving from many of the Algarve towns. But I doubt you'll get as colorful a narration as we experienced from the local fishermen.
