I would highly recommend staying in the Rhapsody Apartments. They're located on a wonderful part of the island, just north of Fira in Imeriovigli. The apartment was great: fully stocked kitchen, nice bathroom, great size, patio overlooking green space below and the water. George was a fantastic host. He'll organize airport transport for just 5 Euro each way and is happy to provide advice for activities. Staying here was a pleasure. (The WiFi wasn't great, but you shouldn't be inside for long on holidays anyway!)