The beaches around the city aren’t up to much, but a short ferry trip will bring you to the Island of Lokrum. This tiny island 700m offshore is covered in a pristine pine forest, dense with Mediterranean and sub-tropical vegetation.
A Benedictine monastery was established here in 1023, only to be cleared out by the Napoleonic authorities during the occupation in the early 19th century. Local legend says that before they left, the monks placed a curse on the island that has led to the tragic deaths of a series of owners. The list includes Archduke Maximillian Habsburg, who bought the island in 1859 and converted the monastery in to a summerhouse only to suffer the misfortune of being packed off to Mexico where he was proclaimed Emperor, kidnapped, and executed just 8 years later. The island has since passed into the ownership of the state (whose misfortunes I don’t have the space to list), and has been converted into a national park.
The Archduke’s Neo-Gothic palace can still be seen, along with its exotic botanic garden and strutting peacocks. There is also the 19th-century Napoleonic Fort Royale at the islands apex, affording excellent views of old Dubrovnik and the sea. The forest offers some beautiful shaded walks. The beaches are very rocky (it will take another couple of millennia before these rocks are broken down into something resembling sand) but they are clean and safe, unlike those on the mainland. There is a small saltwater lake for protected swimming, and a nudist beach (FKK) for letting it all hang out if you so desire.
Facilities are limited to an expensive restaurant and a few overpriced stalls, so bring a picnic. There is nowhere to stay on the island, as this is still considered bad luck. To reach the island, take a taxi boat from the old port. These cost 25kn and leave every 30 minutes, with the last one returning at 8pm. Don’t miss it or you may end up totalitarian ruler of Mexico, and you wouldn’t want that.