I highly recommend Athanasia's apartment! Location is great - just a short walk to the port, and the winding streets of Parikia! Athanasia herself is an absolutely wonderful host -- You will instantly feel like family! When I arrived, she had a bunch of lovely home-made treats at the apartment for me --- Home-made icream, and a special liquor made by her grandfather. Almost every other day, she brought over a new treat :) She made me feel so welcome, and I almost teared up when it was time to leave.
In the summer, having the A.C in the apartment was a life-saver! The shower area is a bit small, but manageable. The kitchen is cute, and has everything you need to cook a quick, easy meal at home.
If you are looking for a family-feel apartment that makes you feel like you have been adopted by a greek grandmother, this is the spot! Location again is fab!