Like most other Aegean Islands, the weather is warm and dry in summer and cold and wet in winter so you should ideally plan a trip in summer. Here is some more information about the weather.
Winter: Winter Temperatures usually skate around the 10 degree Celsius range. The weather is quite cold and the rain might put a dampener on your trip so be aware of this. It is possible to visit all the museums and sites during this time and the tariffs are much cheaper but it clearly is not the best time for a beach vacation. If you avoid the months of December and January, the rain isn’t too harsh either.
Summer: Summers are warm and vibrant. You will find a lot of festivals and events happening during this time. The best time to see Rhodes is in May, June and September, when the weather is warm and sunny. The island gets very crowded in August. Summer is bound to be a super-crowded time though with vacationers from all over Europe flocking to Rhodes. It is also the most expensive time to visit.