Cascais is a good base for touring the Lisbon region but it is upmarket "OK, Yah!" Portugal.
If you want to see real Portugal, and depending on when you are travelling, Ryanair operate Dublin to Porto in the summer season.
Porto is much more traditional and you have the added option of being able to easily visit the historic cities of Guimarães and Braga on day trips by rail or bus as well.
Finally, Ryanair also operate direct flights from Porto to Faro Airport, only 20 minutes drive from the "walled resort!"!
Alternatively, if a second flight with Ireland's Favorite (?) airline, doesn't appeal, the six/seven hour trip by the morning Alfa Pendular Train from Porto to Faro, via Lisbon with a spectacular transit of the 25 de Abril Bridge over the Tejo (Lisbon) would allow you to see a lot of Portugal.
I just have a feeling that from what you want Porto and the North might be more appropriate.
