Not many I fear.
The Algarve Digital project shows that there is wifi available in the lobby are of the Hotel Tivoli Almansor via the PT wifi system
See here: http://bit.ly/9SAQG0
You have to by a voucher. I would presume the Hotel would have them:
Rate here under "Vouchers Físicos":
http://bit.ly/cwGBQG
Also have a look at this old article here:
http://bit.ly/9f4oVe
