Lycabettus is the rock that won. It rears up over Kolonaki to the highest point in central Athens, and from the top the city does the thing it does nowhere else — lies completely flat and open, the Acropolis reduced to one pale outcrop among many, the sea beyond. Go in the evening, for the lights.
Start at Dexameni Square with a coffee, because everything after it climbs. Where the streets give out you choose: the switchbacking pine path on foot, or the teleferik (funicular) that tunnels up from Aristippou. There's no virtue lost in the cable car — the view at the top is identical.
The summit is capped by the whitewashed chapel of Agios Georgios, bells and all, worth a cool minute inside. Then the terrace, and the oh-my-god: all of Athens at your feet, the rock of the Acropolis in the middle, sunset turning the lot gold. Stay for the lights. Come down a quieter pine path on the far side, back into Kolonaki, and walk the gentle slope to Evangelismos.