Even in the off-season, a great number of tourists come to the seaside to enjoy the natural beauty and rest in one of the small Greek tavernas scattered all along the coastline. During the beach season that lasts from May throughout October, you may find great competition for a spot on the seaside, especially on Sundays.
Although there's plenty of beaches between Palaio Faliro and Cape Sounion it still doesn't always satisfy everyone looking for a spot. Some even come on Saturday to reserve a patch of sand for the next day. Moreover, if you come late in the day you are more likely to find nothing.
The peak season is between July and August. The best decision is simply to choose a weekday when the competition is considerable less. Besides, the entrance fee is lower than on weekends.