The dungeon POI map icon shows up as you leave the main eastern road, toward the south. The goal is at the center of the large lake. It is a lone island with a big building in its center. The entrance to the Halls of Regulation is in the northwestern part of the compound, the one you are most likely to come from. The two light posts next to the entrance make it easier as well.
The climate and weather systems of the Clockwork City may be simplified of the weather of Nirn Above, but even simplified, these systems and the mechanisms that drive them are enormously complex.
From the entrance, turn right and go down this road. The path takes you through one longe tunnel, into yet another large room. Even from the entrance of this room, you can spot the Halls of Regulation Skyshard. This is the second largest dungeon room from the south. There is one Kagouti Fabricant next to it, while four Factotum Adjudicators spawn periodically.
Halls of Regulation Entrance
In a junction with three exits in the Halls of Regulation.