Within Garay's area lies Cerro Tres Kandú, which at 842 metres (2,762 ft) above sea level is the highest point in Paraguay.

Its name honors Eugenio Garay, a Paraguayan military figure during the Chaco War, known for being the oldest officer in the army (at 60 years old) and for his major victory at the Battle of Yrendagüé.

There, he led a daring mission of 1,400 men who walked 70 kilometres (43 mi) over three days to capture important water wells, resulting in about 6,000 casualties for the Bolivian army.

It borders the Ybytyruzú Range to the north, which separates it from Colonia Independencia; to the south with the Caazapá Department, to the east with Fassardi, and to the west with Iturbe and Ñumí.

[1] The main economic activity of the district is livestock farming, including the raising of cattle, goats, pigs, and horses.