The best time to visit Osor is during the shoulder seasons, specifically May, early June, or September.
These months offer pleasant weather, with warm temperatures superb for exploring the island and enjoying outdoor activities without the intense heat and larger crowds of the peak summer months. You'll find the sea warm enough for swimming, and the natural landscape is at its most inviting.
For travellers who prefer a quieter experience and good value, May and September are ideal. You can enjoy the historical sites of Osor, such as the Cathedral and the ancient Roman ruins, at a more relaxed pace. The local restaurants and shops are fully operational, but you won't encounter long queues or fully booked establishments, making for a more comfortable and authentic visit.
If your priority is guaranteed sunshine and the liveliest atmosphere, then July and August are also good options, though you should expect higher prices and more people.