On the second day in Dubrovnic, we took the ferry to Lokrum. The ride takes just about 15 minutes and ferries leave every 30 to 60 minutes. There are rocky swimming spots all over and a few sights in the interior of the island. Due to the heat, we did not make it to the fortress but enjoyed the botanical gardens, the monastery (see below), and the peacocks roaming the entire island.
The whole island is a protected area which means that people can not stay overnight and also strictly no smoking. Here is a cute reminder on one of the trails going through the island.