The whole Algarve is at your fingertips. You can reach anywhere on the coast within an hour or so. We spent a day touring the Algarve coast by car. Our favorite spot was the town of Lagos (pronounced in Portuguese as laGOASH). Pretty town, great to wander and shop in the old town, pretty port. While there, ask directions to get to the grottos. We were lucky enough to just stumble on them while wandering. You can get a ~45 minute boat ride through all the grottos and caves for 10 euros per person. It's one of the best things we did on our trip! Will remind you of the Blue Grotto in Italy. We had a wonderfully entertaining fisherman piloting our small boat.
We stayed in the town of Vilamoura. We loved hanging around the marina there. Lots of million dollar yachts, but also lots of restaurants right on the water where you can get a good meal and watch the boats and humanity. There are some good beaches there, but even more so in the nearby town of Quarteira.
Many people love the fortress at Sagres. It's basically the end of the world, the westernmost point of land on the coast. Personally, I found it a bit desolate, though mildly interesting.
There are lots of other things to do on the Algarve coast. Get a good guide book, and read it cover to cover.
