Takes place at the Martello tower in Sandycove (outside of Dublin). Joyce briefly lived there with a friend, medical student Oliver St. John Gogarty) after whom Mulligan is modeled. In Dublin's Temple Bar district, there is a pub called the Oliver St. John Gogarty, and a statue of Joyce and Gogarty is outside of it commemorating their relationship.
This particular stairway in the tower is an extremely narrow, dark, spiral staircase, that leads to the top of the tower. The view from the top overlooks the coastline and the town of Sandycove with Dublin in the distance. Martello towers were used for spotting incoming attacks; there are about 50 along Ireland's coast, many of which are used as locations in works of fiction. The Sandycove tower is now a museum called the James Joyce Tower.