Getting there early is important because the crowds during the high seasons of May to September can be huge. Many of the visitors to the Acropolis come in large waves of tourist groups, so get there early, and beat them to avoid long waits. By noon the sun is hot and the line-ups are unbearable.
Going on your first day prevents two major problems that might come up. First of all if the site is closed due to strike or holiday, then you know you have a few more days to give it a try. The trick to finding out if the Acropolis is closed, is to find the large flag on the East end of the Acropolis, you often see people leaning over taking pictures. If there's no one there, it might be closed. The other reason you should visit on your first day is because of the bonuses you get with your ticket. Your ticket for the Acropolis allows you entry into 5 other sites in the area, including the Agora, a site that should not be missed.
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