Well i should now about my countrie but that i don?t do vacation in the south :) , so i can?t help you if you ask me about the centre or north i could respond, but the last time i had been in Algarve i think it was 15 years ago…
There is a pennisula at the end – I’m not sure of the name Lagos or something … anyway there’s a lighthouse and it can be very dramatic if you hire a car and can scoot around to find some different views of it
Other than that try the local markets for local colour and charachter ..