If you fly to Portugal with your bike, you probably end in one of these airports:

OPORTO INT'L AIRPORT
It's in Oporto outskirts and good if you want to cycle the northern of Portugal or even bike the Portuguese way to Santiago, in Galicia, Spain.

LISBON INT'L AIRPORT
It's within the city limits, ans is also the portuguese main gateway airport.

FARO INT'L AIRPORT
Serving the famous Algarve, it's in the outskirts of Faro and it's easy to bike from there all the way along the Algarve coast and down to Andaluzia, Spain.

FUNCHAL INT'L AIRPORT
If you're into Mountain cycle touring, you have to visit Madeira Island, in the Atlantic Ocean.

THE AZORES
There are 9 islands in the Azores archipelago. The main Airports for international flights are:
LAJES - TERCEIRA island
PONTA DELGADA - S. MIGUEL island
FAIAL - FAIAL island
You can fly to other islands fron these airports.
During summer you can even take a ferry boat linking all the islands together.