The beaches are great for exploration. Beaches outside of town are long desolate stretches of sand with tall cliffs that are excellent for privacy. Many sea caves can be explored during low tide.
Lagos Beach, PortugalWalking along Estr. da Ponta da Piedade a few hundred meters before the lighthouse, (after passing a café and Camila beach on your left), find a concrete fencepost on your right decorated with a spray painted eye, mouth, and two teeth. Enter the path it marks, which will take you to the edge of the cliff. A bit north (to your right) there is a cove accessible only by boat or by a rather narrow hidden mud slope with a rope pegged to the top. There are a number of beautiful, although perhaps dangerous, walks along the top of the cliffs.
Boat tours of the grottos - leave from the harbor for 10 Euros / person
There is also the Praia da Batata in Lagos (right across the main road) which is absolutely beautiful.
You can go on a motorbike and sidecar tour with Sidecar Experience; a breathtaking way to take in the wonderful scenery of South West Portugal