Be aware that there is a spinal motorway (A22 - Via de Infante), that runs the best part of the length of the Algarve.
Consequently, all towns and resorts from Vila Real de Stª. Antonio to Lagos lie within 60 to 65 minutes by car from Faro Airport which is near the centre of the region.
I am sure that the gang here will be up with all sorts of suggestions in this area. I live in Lagos so I am biased but its one of the towns in the Algarve that retains its traditional character.
I know a lot of irish folk have recently been staying here at the Marina Club. (http://www.marinaclub.pt/).
Also have a look at the new Vila Galé Lagos Meia Praia.
www.vilagale.pt/pages/hoteis/index.php?lang=2
They have had promotions on recently.
Another town to try is Tavira, which again has a more traditional character.
