Mercury's Hideout, also referred to as Merc's Lair in the game, is one of the "Bases" for Runners. It was first seen when Faith broke into it when she was still a teenager and was caught by Mercury himself.
Made from a gutted AC cooling tower, it allows concealment and a temporary rest spot (for Faith and Mercury, its a home) for the Runners. The interior (shown only in a few cutscenes) includes several furnishings, like chairs, tables, and a noticeable decent-sized red couch. The exterior seems to allow protection from stalking Helicopters as well as weather change. One of the main things about the place is the multiple computers fitted inside. Merc uses them to hack into city cameras and use them to help Faith along the way of her tasks and objectives. After The Edge, Faith is seen listening to police radio and stacking a card tower.
In the Mirror’s Edge comic, Merc and Faith reside in a separate Hideout within a set of air vent boxes on a building’s roof.