I am in the process of making up a list from various sources. So far I have found no where around there. The nearest I have so far are below. Whether or not they are free I don't know except in one or two cases.

Algarve Shopping Mall - McDonalds and FNAC

Albufeira - any post office but what you are supposed to do to use it is mystery. Sit outside? Can't sit inside. Pay sites.

Albufeira - ditto the telephone shop near the Camara. PT wiFi - pay

Albufeira Marina - not sure exactly where though.

There are others.

Unlike some of the smaller towns in the Algarve, Albufeira does not have a free public wi-fi hotspot courtesy of the local council.

Meanies.

did you ever find anywhere for a bit of wifi use?

There is now a free public wifi service (Algarve Digital) around the Camara (Town Hall) but you cannot sit down anywhere to use it!

I picked up two wifi services at Albufeira McDonalds near the Camara. One was the PT WIFI service emanating from the nearby post office (free to me as I have an account anyway) and the other was Vodafone, perhaps from MCDonalds itself.

There are a few bars and restaurants that offer free wifi service to customers, so things could depend where you are staying.

I haven't been into any of the internet cafes to see if they offer wifi.