Faro is the administrative capital of the Algarve and while you will find plenty of shopping there, both in town and in the Algarve Forum Shopping Centre it is not exactly what I would call a holiday destination.
It is a ways from the coast...the local beach is about 8km away at Praia de Faro.
Don't know where you got the idea that most places will be closed! Faro is the one place in the Algarve where most shops and restaurants will be open at this time of year.
