I'd love to help you. I have a 4 year old, but traveled with her to
Greece when she was 6 months and up, and we live here now.
1. I'd like to say that
Greece is "child" friendly, but there are a few frustrating things. The streets are not very accomodating for strollers, so I'd recommend a kangaroo pack, or something you can carry your child without the need of a stroller. When you rent a car, they do have car seats, but I would book this in advance. I've not found any specific laws for actually using a car seat, but do know that children are not permitted to sit in the front seat.
2. It's very rare to find a restaurant with highchairs, so keep this in mind. When we visited the islands, we would take our stroller just so that we could feed our daughter in her stroller when going out to a restaurant. Jars of baby food are available and I do know they have various baby cereals and milk powders.
3. You've picked beautiful islands to visit. The weather will be warm in May, but not necessarily the water.in fact it might be on the cooler side. Generally speaking, Santorini and Myconos are "celebrity" type islands and known for being party islands. Given that you're traveling with a one year old, they don't require much entertainment necessarily, so I don't think you'll be disappointed when you don't find any Disney type
hotel offerings. It's all about the view, the sea, the calm, the people. Local shops sell all kinds of water/beach type toys. Also keep in mind most restaurants start much later in the evening, very typical for people to start their dinner at 10:00 pm.
4. There is no such thing as a "family"
hotel, all hotels accomodate children so to speak. What you may be interested in getting though is a
hotel room with a kitchenette, that way you won't be bound by any breakfast rules, and you'd be able to heat of a jar of food and such. Perhaps a
hotel with a pool that way if you find the sea is still too cold, you'll have an alternative.
5. Definitely bring lots of sunscreen and hats. On the islands at night there's a good breeze sailing through so I'd definitely bring some warmer cloths for night, like jackets. As for the water, as I said before, the sea might be a bit cooler in May, but playing in the sand will be a joy! Drinking water is heavily flourinated in
Greece. You can make a coffee with tap water, cook with it, but if you drink water on it's own, you will consider purchasing it. No problem with the milk, and it comes in many fat levels.
If you have any other questions, let me know!