There are taxi stands scattered throughout Athens, but more often you will end up hailing one. This can be an adventure-and not always a pleasant one. Taxis are required to pick up as many additional passengers as possible going the same direction, so the taxi driver is unlikely to pick you up unless you are going that way too. Don't give up if the rooftop light is turned off. Exercise caution in the matter of fares.
Some taxi drivers are unscrupulous.
Check the meter to see that it is registering properly. If the taxi picks up other passengers, everyone will end up paying the fare on the meter up the point where he gets off. If you are last in and first out, you may try to negotiate your part of the fare. The rate may be slightly higher, but it is worth it. When flying through more than three time zones you circadian rhythm can be thrown off-gear.