After a rather bumpy boat ride (about 1 hour) from Peniche, you'll arrive at the deserted island of Berlenga. There's a restaurant and a few chalets but beyond that, the main inhabitants are the seagulls and other wildlife. You can sit on the tiny beach among the seagull poop or take a glass-bottomed boat to explore the cliffs and caves.
The best thing, in my opinion, is to explore the island on foot. You'll discover beautiful flowers, dramatic scenery and a picturesque fort.