If you want to get away from the backpacking tourists, head to Vila do Bispo. It's about an hours bus ride from the garage. From the Vila do Bispo bus stop it's about 5 kilometers to the beach. It's not a bad walk, and there are hiking trails that head off into the hills if you're interested too. The beaches are gorgeous and seem to never end. Beaches are clothing optional, but most people are clothed.
Beaches of Salema and Luz, both outside the city.
Monchique town/spamountain.
City of Silvesmoorish castle.
Burgau, lovely example of a traditional fishing village and fantastic beach.