The Algarve hasnt the greatest scenery ,though i'd second the above comments,especially Monchique area (Forested back roads are quite nice).
If you don't have young kids you may consider the 250 kms drive to lisbon on the new motorway; locals tell you it takes two hours -took me three with short break.
Faro,much ignored, has nice old centre and further east towards Spanish border try the pretty town of Tavira.
strange how Portugal has the highest traffic fatality record in western europe.
Like others above I found driving easy.