Greece has numerous islands, of which 277 are inhabited. The most popular amongst them is obviously Santorini. Being the most popular and busiest, there is always huge traffic on the island in most parts of the year. It’s difficult for me to say if you do not want to see too many people then visit in May or October because when I visited in May there were lots of people.
So I wonder what it would look like when you visit in July August or December. Any which way, if you’d like to see a relatively small crowd, then your best bet is April May or October November. You may find cheap hotels easily during these periods. Also during these times, the hotels and restaurants are not too busy, the prices of items are relatively cheaper and you can get beautiful spots to take wonderful pictures.
During peak seasons, one may struggle to find a seat in a particular restaurant. Whichever month you decide to visit, be ready to stay in queues to take pictures of the places mostly advertised on the internet. You may stay in queues because they are the spots everyone wants to take pictures.