The Ilissos River lay outside ancient Athens' defensive walls. Today the river has been canalized and is mostly under ground.
The only section of it still available for vistors to see is a small area on the south side of the support walls of the Temple of Olympian Zeus. The river has 2 sources: the upper slopes of Mt. Hymittos near the Kessariani Monastery and in Kareas by the church of St. John the Theologian.
Ilissos, a demi-god, son of Poseidon and Demeter, was worshipped in a sanctuary on the Ardittos Hill next to the Olympic Stadium (an area popularly assumed today to be haunted but by later spirits as the Nazis had a an HQ near bt during WW II).
In ancient times Athens was a bit more idyllic and there were several temples, bridges and sanctuaries to Nymphs such as the Kallirhoe lining the banks of this river.
Modern Athenian brides to be are still called nymphs in modern Greek: "Nee-phee".
For more on the Illissos River and Kalirhoe Spring read the Syntagma Sq start here page.