Kolonaki is where Athens dresses up. It climbs the lower slopes of Lycabettus in a grid of designer streets, small galleries, and café squares, and it knows exactly how good it looks. Walk it in the afternoon, when the gallery doors are open and the square is settling into its long, watchful evening.
Arrive up Voukourestiou, the jeweller's street, and let the city change register as you climb into Kolonaki. Plateia Kolonakiou is the hinge — take a table, watch the volta (the evening stroll) begin. Then the gallery streets, Skoufa and Anagnostopoulou, where contemporary spaces hide between the boutiques and most will wave you in for free.
The two museums are the weight of the walk: the Benaki for the sweep of Greek history in a neoclassical house, the Cycladic for the spare marble figures that look three thousand years ahead of themselves. Do them lightly. Finish up the leafy steps toward Dexameni, where the quarter goes green and residential under the hill, and drop down to Evangelismos.