Athens has enough ancient history to fill a week, but one day is enough to hit the icons if you move early and stay focused. This itinerary sticks to the Acropolis, its museum, and the historic center around it, deliberately skipping the National Archaeological Museum, Kerameikos, and other worthy sights that simply do not fit into a single day.
Arrive at the Acropolis right when it opens to beat both the heat and the tour buses, and spend the morning taking in the Parthenon and the Erechtheion with its famous caryatids. Head downhill to the Acropolis Museum for an hour to see the sculptures and friezes up close before the midday crowds arrive. From there, walk through the Ancient Agora and the nearby Roman Agora and Library of Hadrian, pausing at the Theatre of Dionysus on the way. Grab a quick lunch in Monastiraki, then browse Monastiraki Square and its flea market stalls. In the early afternoon, walk past the Temple of Olympian Zeus and through Hadrian's Arch, then swing by the small Byzantine churches of Panagia Kapnikarea and the Church of Agios Eleftherios tucked beside the modern Cathedral of the Annunciation. As the day cools off, walk to the Panathenaic Stadium, the site of the first modern Olympics, before finishing the evening with a stroll and dinner around Syntagma Square.