The best and cheapest transportation from Mactan International Airport in Cebu to Cebu City is by taxi, not just any taxi but the metered taxis.
Don't forget though that not all taxis are the same. You do not want to get a taxi from the stand at the airport. To access the cheaper taxis, once you exit the airport at the front, go across the road you face. On the other side of the road there are some stairs, climb those stairs and you will come out and face another road.
Here you will find more taxis, that are not on fixed pricing and will use the meter, well they will use the meter if you ask, make sure you do, if they refuse hail another cab. They are required to use the meter.
Personally I have found the white taxis to be more accommodating than the yellow ones, not sure why?
