Most main centres have Internet Cafes.
Portugal Telecom does have a public wifi service available in selected hotels, post offices etc throughout the country.
Have a look at this link:
http://www.ptwifi.pt/localizacoes/default.aspx
You buy a card starting at € 5.00 for 1 hour which you use to access their network through your browser.
Certain towns also have locations where the council offers free wifi access. e,g, here in lagos free wifi access is available at the Cultural Centre.
