My selection:
Acropolis, Athens - iconic, YES Agrigento - I prefer Paestum, NO Aigai (Vergina) - YES, for the best preserved Greek burial site Delphi - of great historical importance, but less remains, NO Butrint, Cyrene, Delos - no for all three Ephesus - Yes, but for both Greek and Roman remains Epidaurus - No, enough theatres Hierapolis (-Pamukkale) - no Mycenae/Tiryns - Yes, for Mycenaean culture Olympia - mostly intangible importance, no Paphos - for its Greek mosaics, Yes Samos (Pythagoreion and Heraion), Tauric Chersonese - No for both Bassae - Yes, for its excellent preservation of a Greek temple Troy - Yes, for its importance in the history of archaeology
Pergamon - maybe Paestum - Yes |