The President's mansion is a location which appears in all three books. Found in the City Circle, it is home to President Coriolanus Snow, and briefly, President Alma Coin. After being elected new president of Panem, Paylor presumably resides there as well.
In The Hunger Games, the tributes ride their chariots through the City Circle and stop in front of the mansion to listen to a welcoming speech given by Snow. In Catching Fire, it serves basically the same role. Following the end of their Victory Tour and arrival in the Capitol, Katniss Everdeen and Peeta Mellark attended a grand party put on in the banquet room. When Plutarch Heavensbee danced with Katniss he showed her his watch on the pretext of indicating the lateness of the hour and quickly flashed an image of a mockingjay by rubbing the watch face. This was a subtle hint at the nature of the 75th Hunger Games arena as well as Plutarch's true allegiance to the rebellion.
In Mockingjay, Katniss tells her squad that she was on a mission to infiltrate the mansion to kill Snow on Coin's orders. However the squad never does infiltrate the mansion, because President Snow surrenders to the rebels after a hoverplane with a Capitol seal on its side drops bombs on the Capitol children and some rebel medics, including Prim. Later, the mansion becomes the new home of President Coin. Katniss wakes up inside the mansion, and goes to the rose garden, where she meets some rebel soldiers guarding it, but Commander Paylor tells them to let Katniss in. Inside she finds Snow, shackled to a chair and awaiting execution. Snow tells Katniss that he himself did not order the bombing, rather, Coin did to force the Capitol to surrender. Later, the surviving victors meet and vote to have a Hunger Games including Capitol children. Immediately following this, Katniss was to shoot Snow with an arrow (firing the symbolic "last shot" of the rebellion), but shoots Coin instead to avenge Prim.
The President's mansion is very large and Katniss presumes it to be full of pods to discourage intruders. It contains a garden, where Snow grows his genetically enhanced roses and where both he and Coin are killed. It also contains a ballroom, and a meeting room where the surviving victors decided whether or not to have another Hunger Games.