PLEASE IGNORE THE ANSWER ABOVE (apart from the bit about bus services)!
Those taxi fares seemed so ridiculous that I've taken another look at the information on the Faro Airport website. My post correctly quoted the fare given on that site but there must be an error because the fares to places much further away are far lower than the Fare to the centre of Faro!
You can have a pre-booked car waiting for you, to take you into Faro, for 20 euros. Book here:
http://www.polotur.com/
Chris