TRAIN 

Two train stations are in walking distance from Proa d'Alfama guest house : Cais de Sodré & Santa Apolonia.

The train is ideal to visite Belém, Cascais & Sintra. 

The are no options from the airport by train.  

Here is the national railway website : www.cp.pt

TAXI

From the airport

A taxi from the airport can cost between 18 and 25 euros depending on the time of the day. 
As you come out of arrivals, take any exit in front of you to get to the taxi pick up.