Generally, Athens is a very safe city. Many of the homeless or the drug users, may seem dangerous but the truth is that they are completely harmless. You just have to use a common sense, like every other european capital. Many Athenians avoid areas like Omonia, Vathis square, Metaxourgio, Exarchia, Agios Pantleimon, at night, but violent attacks are rare. Of course, a lot of women avoid walking alone after 23:00. The police are almost everywhere in the city centre and you can trust them.