Like all Cycladic islands, there is a season for the tourism. The tourist season in Amorgos kicks off around Easter and ends around late September. As Amorgos is not a popular island like Mykonos or Santorini, the season ends earlier here. After October, many of the hotels and restaurants will already close so even though the weather is still great, you won't have much to do. July and August are the busiest times of the year to visit Amorgos but it never gets overwhelming like other islands in the Cyclades. The best time for me to visit the Cyclades is May and June as well as late September when the crowds are dispersed.