Having lived in the Algarve for 4 years then of course I can recommend that..but not so much the busy parts around Faro. Its also very warm in summer.. If your looking for some nice scenery and relative quiet then try the Western Algarve and the west coast around Sagres and Cape St Vincent. Lagos is a pretty and relatively unspoilt city with loads of history. Unless you want British food and to bump into loads of Brits I would avoid Praia de Luz.
The bit of Portugal between Lisbon and the Algarve is called the Alentejo and not only produces nice wines but also has some pretty scenery near the Algarve.
Moving across into Spain I would also recommend the Granada and Alhambra areas for touring.
