Giannis house in Aerinos is an excellent option if you want to be close to Elafonisi (and the rest of the popular beaches) but away enough from the crowded/touristic places. Its an amazing location high in the mountains with an excellent view and atmosphere. It can get a bit windy, so pack a jacket just to be safe :)
Gianni's grandmother is an amazing person and an excellent host. She is by far the best kaltsounia maker in Crete. So be prepared to taste some delicious treats.
Also, Margarita (the family dog) is a great company and hugs giver.