Hi!
Bld211 is right!
You are going to be hard pushed though to get to one of the large supermarkets if you are arriving 11ish as by the time you've cleared immigration, got the car etc, it could be precious close to 13:00.
If you clear the airport by 12:15 head for Jumbo in Faro. Instructions on my blog here:
http://barlaventostravelblog.blogspot.com/2007/07/algarve-late-night-arrivals.html
If you do not make it head for Lagos along the motorway. Take the exit for Lagos Este. Follow the exit road for 4km until you come to a roundabout. Turn right and follow the road into Lagos until you come to second roundabout (With Fountain in Shape of a caravel).
Turn left into the center passing the Galp Service Station on your right. Continue straight over the following roundabout - you are then on the main Avenida. About 1 km further on you will find on your right a supermarket called Marrachino. They are open all day Sunday and will at least provide you with your immediate needs.
To getback to PDL continue along the Avenida, up paste the Fire Station and the road will eventually lead after 7 kms to traffic lights where you can turn left to Praia Da Luz
