"Home" The one word that seemed to define every moment of Harry's life. A word that in reflection Harry didn't have much of.
Privet Drive was understandably not home. It was a house in which Harry had lived, or really rather stayed. The house no matter it's numerous windows would only ever been seen as a dark dreary place that smelled of the lemon cleaning product he'd used from a young age to clean the house. Privet Drive was immortalized in the stinging pain of hunger, forced labor, and harsh words. It was Privet Drive where Harry learned that sticks and stones really do break bones, but names or more over words could flay you alive without the threat of death. Words hurt worse than being cut open with a knife leaving you hurting and struggling in pain but knowing that you'll live another moment, there was no sweet release of consciousness due to blood loss to lessen the blows. The cupboard was a safe place in the house, a temporary retreat from the pain, but not fully, because everyone in the house knew that was Freak's room, Freak wasn't like the Dursley's so Freak had to be hidden away. Privet Drive was never home to Harry Potter, merely a place in which he had existed for a span of time.
Hogwarts had a feeling of home, at least at the start it did. It was a safe space from the Dursley's. The first Quidditch match took that feeling away, suddenly he was no safer there than he'd been at Privet Drive, it was like being in his cupboard, he was safe from Vernon's temper and Petunia's beady eyes, but that didn't mean he wouldn't be hurt. Second-year made Hogwarts a hell comparable to Privet Drive, all feelings of relative safety were gone. He'd traded Vernon's temper for the fickle temperament of the wizarding world and Petunia's beady eyes became the eyes watching him, judging him all because he survived when his parents didn't. No one understood that he'd give up his fame and any gold in his vault to have his parents, not even Ron who was his very first friend. The only safe place in Hogwarts was Snape's class, even though the man was a right bastard and had a temper to rival Vernon, he made his dislike of Harry clear from day one and didn't change his tune like everyone else, he was verbally abrasive, but still, he tried to help keep Harry alive. In the end, Hogwarts was a battlefield where he lost people that he'd come to care for and even the safety of Snape's class was tainted. Hogwarts was a place Harry could no longer bear to look at.
Grimmauld Place could never be considered anything but a resting place between tragedies. The first time he ever saw the place was just after the dementor attack while waiting for his trail, the next just after Mr. Weasly was attacked, and finally after the attack on Bill's wedding. There was no safety in the house, no feeling of home, it was Sirius' second prison, a place to rest a weary head before the next trouble befell you. Sirius had been the only good thing about the house, but it was more the man himself then the house, and even that didn't last long.
The Burrow was someone else's home, so Harry never tried to think it could be a home to himself. It was full of life and love, a constant energy seemed to pour from its walls and it was all too easy to think of it as home. The first real, lasting place that Harry felt at home. It was there that Harry had his first birthday party. After the attack during the wedding Harry could still think of it as home, after all, they were working to end the war, soon those that attacked before would no longer be a problem. The Battle of Hogwarts killed that feeling of home in the Burrow, now it was full of sorrow and mourning for the lost, the Burrow could never feel like home when there was a hand missing on the clock.
Godric's Hollow, Harry would suppose, had been his very first home. His mother and father had lived there with him, for however short a time. The only memory Harry had of it was his mother screaming and so he could never look at it as anything but a resting place for two brave people who gave their lives saving their only son even if they had no way of knowing if he'd join them only moments later in death.
After the war Harry never returned to Hogwarts, nor Privet Drive, he visited The Burrow only once, and Godric's Hollow every Halloween. Grimmauld Place was left empty with a house elf assigned to clean it once a week so it could be kept nice for Teddy, whom Harry made Heir Black. He tried to find a home in his life with Ginny, they bought a house, eventually, they married and had children, but the house was just a house. No matter how much it bugged Ginny when he never said: "Let's go home" and always "let's get back to the house" or even just said the street name, he couldn't call it home. It felt wrong, the house was full of love and life and even had that energy The Burrow once had, but to Harry, it still didn't feel like home and he had no idea what was missing. In his heart of hearts, Harry had given up on the concept of home. Home was just too easily taken away.