I travelled with my 5 year-ols child, and I have to say that Santorini was a perfect choice. It's a very safe island (unless your child is clinmbing everywhere) and people are all very kind to kids. Special thanks to the suite's staff who were all so lovely with him.
We had a wonderful stay at the secret gem suite! Everything was just perfect, from the communication at our arrival to our transfer at departure. The staff is there for you. They set up everything (the visits etc), and are very good advisors.
The place is gorgeous! A little cocoon with a bath tube on the terrasse. It's at Amoudi bay thou, so to join Oia you will have to go up and down 250 steps. But it's worth it! you'll be staying in a quiet area, next to the best fish restaurants.
The suite is furnished with evrything you need (even toothbrush, shampoo etc) and the towels changed everyday. The breakfast is huge (you'll have enough to carry with you for lunch)
I would hardly recommand this host, either you are travelling with your family (like I did) or your lover (very romantic view on the sunset)
My son disn't wanna leave... so I guess we will have to come back one day!