If I were you, I’d start with the big classics of Rhodes itself: the Old Town of Rhodes, Lindos with its acropolis, then a more nature-focused day at the Butterfly Valley. These are the most popular visits and they strike a great balance between culture and beautiful landscapes. For the surrounding islands, Symi is definitely the most obvious and prettiest day trip, and Halki is a good option too if you want something quieter. As for the weather starting May 18th, it seems like a really good time overall. When I was looking into all this, I used these pages to get an idea of the sights and ferry crossings: here and here, for example