What's a good topic to write on for Greek tragedies?
Even though you may not feel prepared to write a paper on Greek tragedies, this is an excellent opportunity to learn some really interesting things. Your teacher gave you license to choose anything you want, so I would suggest you follow your interests. I have no idea what your length requirement is, so some topics may be out of the question for you. Here are a few ideas.
The Greek theatre. How is it different from today's theatres and amphitheatres? How are today's theatres similar to those of the Greeks?
The Greek actors and staging. What they wore and why. There are some really interesting things to be discovered here, as this is the inception of the "drama masks."
The Greeks and theatre. How did the Greeks view theatre and tragedy? For example, they held festivals which were essentially drama competitions (among other things) funded by rich businessmen and free to the public.
One other aspect of Greek theatre--and tragedies, in particular--is that the audience generally already knew the story before they went to see the play. This adds a delicious irony in Oedipus Rex, for example, when they know beforehand what the main character does not. Irony in Greek tragedies is a significant topic for study, as well.
The eNotes site I've included below is a great starting place for all kinds of things connected to Greek tragedies. Best of luck!