Lokrum Island is about a 20-minute ferry ride from Dubrovnik's Old Town Port. It's a park, really, with a cafe, trails, an abandoned Benedictione monastery, and swim ladders along the shores. Sorta like Central Park for Manhattan but with swimming and sunbathing.
In June, the Adriatic is not warm but refreshing and comfortable. We met Aussies and Californians in that pictured beach.
The Croatian coast is almost entirely rocky which is why they put swim ladders on the rocks. The rungs are slippery and hurt your feet so if we ever go back we'll bring water shoes. Yes, the boat swim ladders are the same.