Just a ten minute ferry ride from Dubrovnik is the Island of Lokrum. Lokrum is a nice natural island where cars aren’t allowed. You can walk the trails of the island up to a fortress where you get a nice view of Dubrovnik. They have a small botanical garden on the island, however most of the plants are not native. Someone donated a lot of peacocks to the island so they roam around looking for food from people. I was one of the crazy tourists that started taking pictures of the peacock as soon as we got off the boat.
We were told there is a nice beach there but every beach we ever saw was just a ladder down into the rocky sea. We sat on the rocks for awhile and just watched the waves crash on the rocks. Lokrum was worth the visit (and a nice place to get away from the cigarette smoke).