We where in Lindos in October and had a terrific time here. Weather was still good and since it was end of season there where a little less people in the town (but everything still open).
The place is located just perfect in the middle of the village - and the sandy (!) beach is just a 5 min walk. The apartment looks very authentic and traditional. It has a large patio in the middle from where all room are accessible. We felt home immediately and would come back anytime.