The Acropolis is, of course, unmissable, as are the Acropolis Museum, the ancient Agora and the National Archaeological Museum. Other ancient sites one might visit are the ancient cemetery of Kerameikos (the potters’ district, where all those ancient painted Athenian vases you see in museums...
Some more info about your interests would be helpful. Are you interested in art? Antiquities? Greek history? None of that? What *do* you usually like to visit in a European city?