You wrote that you are trying to decide whether to go on a Greek cruise to the Islands in Sept/Oct or May/June.

Both periods are equivalent concerning the weather: May <== > October June <== > September

Avoid April and the first 2 weeks of May. It may be the Greek Easter (this year Easter is at 23 April), where all the local people leave the towns, so the tourist areas are overcrowded and the prices high, and it's not sure the weather is so good for swimming.

The advantage of the spring is that the day is longer and there is sunlight for more hours than in the fall.

Both periods are not high season, so the prices are similar.

In exception: for Santorini September is high season, because many European tourists (especially retired) choose that period to visit the island.

Maybe in the beginning of September some tourist areas (like Rhodes and Mykonos) are still crowded.

In your case I would prefer to visit the islands in June.

Happy Trips and Best Regards from Athens, Joanna