I would suggest Lagos.
Look at the Vila Galé Hotel Meia Praia, Lagos. - http://bit.ly/8tbzzQ
Vivenda Miranda at Porto de Mós is also well situated. - http://bit.ly/7c2JYk
Finally, the Hotel Baleeira in Sagres may also be of interest. - http://bit.ly/7gLh3I
The Western Algarve is less developed, and Lagos retains more the feel of a traditional Portuguese town than many other places along the Algarve Coast. The West coast with its hidden beaches and rugged coastline is a great place to explore.