List of wifi locations in Vilamoura:
See:
http://v4.jiwire.com/search-wifi-hotspots.htm?result_display=list&technology_id=0&venue_group_id=0&city_id=0&disableBrowseBy=false&type=&state_id=0&city=&address=Vilamoura%2C+Albufeira+8125%2C+Portugal&latitude=37.0751581&longitude=-8.129496
Does not look like there are any free ones.
According to AlgarveDigital, there are two free wifi locations in Quarteira, right next door to Vilamoura.
See:
http://www.algarvedigital.pt/algarve/index.php?module=Access%20Point&func=view&id=8
and
http://www.algarvedigital.pt/algarve/index.php?module=Access%20Point&func=view&id=85
Be aware that as these are in council installations, range may be limited and you may have to perch on a bollard outside to use the service!
