There is more than variety of selection of events in Athens. A good question is where to find out about them, since most content is still in Greek, and there is no official calendar for Athens’ visitors. Even though, we will make an effort.
One special source is the Athens’ official page with information for events, here.
Besides them, Athens houses some main events, like Marathon on November, Athens festival during summer, Easter in Plaka of course, Apocrea on February, there is also the military parade of the Indepedence War of 1821 on March 25th, that is a national holiday as well. On September there is Athens Flying Week, where you can see airplanes above Athens or even visit military airport of Tatoi (you could combine it with a visit at Royal Palace there).
Moreover, there are spots like Megaron (in the metro station) for music events mostly, modern Onassis’ Foundation Stegi and also Stavros Niarchos Park that offer numerous activities, info about them you can have at their website. Some of them are also free, so keep it in mind!