This square is the shame of my city. Once (decades ago) the most buzzing area of Athens and cultural center. Today, if you are a family or a couple or group of women (or even worst a single woman) better stay away of this place (specially at night!). Trust me is worth to pay little bit more in some hotel elsewhere than to stay there (is full of any kind low rated cheap hotels at Omonia area). If you are a group of boys/guys with urban background and you know how to "move" careful in this kind of areas you are some kind more safe but don't pull it too far with nobody cause all the streets around the square at night is full of thugs (among with prostitutes, junkies, drug dealers, homeless locals & immigrants, etc. ) ready to get in any "action" they can find or get called to join.. But of course as i said, if you can avoid to stay there just do it. The "Souvlaki" things around the diameter of the square is 100% dreadful so definitely avoid them also. Better eat a bag of chips or something.
Hint: Omonia square is connect with the famous "Monastiraki" area (below Acropolis sight) by a street called "Athinas" (1km in total) which is the most commercial point of Athens for (mostly) food supplies. Is safe at day light and the cross streets hosts the best shops of the city for local (and imported) spices and herbs.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.