The Ancient Agora was the living room of classical Athens — market, law court, parliament and gossip-ground, the place Socrates worked the crowd until the crowd condemned him. It also holds the best-preserved Greek temple on earth, and the gentlest pedestrian promenade in the city loops it. Go in the morning, before the heat and the tour groups.
Enter off café-lined Adrianou and start at the Stoa of Attalos, the marble colonnade rebuilt whole in the 1950s — walk its upper floor and read the small museum's voting tokens and exile-shards. Then cross the open Agora floor, low foundations and gravel where the democracy ran, to the Temple of Hephaestus on its rise: Doric, near-complete, the column-rhythm intact. Circle it for the view back to the Acropolis.
Leave by the Thiseio gate onto the Apostolou Pavlou promenade, car-free with the rock at your shoulder the whole way, and follow it to the Thiseio rail bridge, where the line frames the Acropolis and Line 1 takes you home. A drink under the bridge first, if the light's gone gold.