If the weather is nice and you have around 30 Euros, you can charter a day trip from Grand Baie to Ile Plate or Ilot Gabriel. As the boat heads north, it passed by the famous Coin de Mire and then continues another two or so hours towards Ile Plate. When you finally arrive, you feel like Robinson Crusoe! Most tours also include a barbecue of fish and met right on the beach and a day full of swimming and snorkeling in the lagoon. It's literally like spending a day in paradise!
If you don't know this small island belonging to the Republic of Mauritius, take my advice: book a ticket and begin your dream trip! An authentic population, great beaches and no mass tourism! A place to discover!