Definitely consider Skala Rachoni, as Leanne suggested, because it may be exactly the type of resort you’re looking for. It doesn’t get as crowded as some of the other resorts on the island, even in the peak summer months. Many locals I know go swimming in Skala Rachoni for this reason. The beach is long, sandy, and very shallow. There are many excellent tavernas along the coastline and there are some swimming pools as well.
These are a few of our lovely, more quiet resorts with organized child-friendly beaches and a good selection of tavernas. To be at a walking distance from the beach and tavernas will depend on the property you choose to stay at.