Driving is pretty easy there. We stayed in Lagos and rented one near the end of our stay to do a few day trips and drove to Lisbon where we ditched it.
I think if you have the time, you'd be missing out if you didn't drive to the westmost point where the lighthouse is, and just east of there, the fort remnants where Henry the Navigator was based.
http://www.algarve-tourist.com/Sagre...gres-fort.html
The rocky coasts are really amazing if you are into Geology, and the raw western winds are powerful.
Further up the coast some of the beaches are gorgeous like Praia do Amado(surfing) and Praia Da Bordeira.
Lagos is great too, go to the dock and pay a fisherman to take you out around the point for an hour. Or drive to the end of the point and walk around the trails.