Castelia Sewers is found by an entrance in Castelia City on the pier near the Gate Bridge, located in South Unova. Hugh will join the player as a partner when you explore the first time. And also, for the first time, you will meet Colress.
The Relic Passage can be accessed from here.
There is also an exit to Castelia City's park with wild Pokémon, and when the sewers are flooded, to Castelia City's back alley.
During autumn and winter, the sewers are dry, blocking some areas and removing the requirement of Surf to access others.