Nothing is known about the the Governor's apartment or who initially owned it prior or during the outbreak, except that it used to be part of the town's residential area.
After Woodbury was secured from walkers, facilities were being built or re-established to keep the citizens within its walls idle. One of these would be the Governor's apartment, where he resided during his rule on Woodbury. Aside from being the Governor's home, the apartment also became his office to fulfil his role as the town's leader and also the place where he kept his daughter, Penny, along with his collection of the decapitated heads of his victims.
The morning after the arrival of Andrea and Michonne in Woodbury, the Governor invited them for breakfast along with Milton Mamet, who asks and fails to learn about Michonne's pet walkers. The breakfast is cut short by Philip as he has some important matters to make.
The Governor looks over Woodbury from his apartment window as he sips from a glass of whiskey. Rowan is seen naked on the Governor's bed, indicating that they are in a sexual relationship. He enters what it seems to be a private room. Inside is a collection of amputated heads stored in three rows of aquariums. Among them are the heads of Michonne's pet walkers, as well as the head Lieutenant Welles.
In this episode, the Governor is seen brushing a girl's hair who appears to be his undead daughter, Penny. He immediately restrains her after he accidentally takes off a piece of her scalp.
Later on, Michonne is seen trespassing in the apartment to retrieve her katana that was kept by the Governor for safe keeping. She stumbles across a journal with the objectives and plans he has for Woodbury and a list of names of people he knew who had passed on, the last name being Penny. Michonne then hides and overhears the discussion of the Governor, Milton, and Merle Dixon regarding their plans for that night.
Andrea is summoned by the Governor to his apartment to talk about the incident on the town's wall. Eventually, the discussion goes to how Andrea liked the arena fights and how Philip thinks that she likes him.
Later on, the Governor and Andrea are seen having sex but are interrupted by Merle reporting that Michonne was "killed" and that he brought two captives (Glenn Rhee and Maggie Greene).
After Andrea mentions that she's going to help Milton cremate Mr. Coleman and leaves, the Governor goes to his private room to open the cell where his undead daughter is caged. He sings a lullaby for her then realizes that Penny is distracted by a bucket of meat. This causes Philip to be frustrated as he tries in vain for her to remember him. He then thrusts his daughter back to her cell.
Back at the Governor's apartment, Michonne discovers his secret room and unchains Penny, thinking it's his daughter and he has locked her up, before realizing she's a walker. As she positions her sword to kill Penny, the Governor comes in. "Don't hurt my little girl," he pleads. Michonne, disgusted and vengeful, stabs Penny through the head. The Governor, overwhelmed with grief and anger, then attacks Michonne in a rage. As the two grapple, the aquarium of walker heads is smashed. The Governor starts choking Michonne before she manages to grab a shard of broken glass and stabs him in the eye.
The Governor reels as Michonne prepares to finish him off with her katana. But then, Andrea walks in and draws her gun on Michonne. The two face off, but ultimately, Michonne flees. The Governor cradles Penny's body, devastated.
In the Governor's apartment, Andrea urges him to reassure the residents after the attack in the arena by the prison group. Later on, residents begin to crowd in front of the Governor's apartment about the safety of the town, whom Andrea and Milton are able to pacify. Unbeknownst to them, Philip looks down on them from his window.