Harry Potter felt the decisions regarding his mental well-being, studies, and finances were the most immediate tasks. The planning he had done for them will suffice for now, and the details will have to be adjusted according to various people's responses.
The next big change he felt needed in his life was his personal relationships. He had wanted Hermione since the end of 3rd year, but every time he thought of talking with her about them, something or someone derails his plans.
In the 4th year, he finally had ample private time with her due to studying and practicing for tasks. He had thought of asking her to be with him after the Yule ball. That was shot down when he learned that she had already been asked by someone and had said yes to him. It infuriated him so much; the girl has such confidence issues in herself that any stranger could ask her for a date and she says yes immediately. Then Dumbledore, in his typical way, chose Ron as his 'most important person to save' for the 2nd task.
The 5th year fucked him in more ways than one, No one contacting him throughout the summer vacation had made him extremely angry and disappointed in his friends. He had expected something like this from Ron and the Weasleys, but not from Hermione and Sirius. Then the court case, nightmares, and Umbridge happened. Who had time to think about relationships when so much shit was happening around him.
Hermione's deferring to the authorities after the 4th year had ended, made him realize that he could never tell her about his growing friendship with Daphne Greengrass. Daphne had been a breath of fresh air during the 4th year fiasco with her calm and collected response to his impending tasks. He was the one who had approached her in the Hogwarts Library and sat opposite her without even saying a word. It was done so that he could get a moment of peace and study without inquisition and all the stares that had followed him after his name came out of the Goblet.
In the 6th year, he finally had time to broach the conversation between Hermione and him. But as usual, fate conspired against him, Hermione had decided to pursue Ron by some convoluted logic that only she could justify. It was not as if Harry didn't know that she didn't love him, the times she had stuck with him despite all the challenges was easy proof.
Hermione had always understood him on a level that no one else ever had, their closeness to each other after rescuing Sirius, could be seen by everyone in Hogwarts. The intimacy in their conduct and conversations was an easy giveaway to their compatibility and feelings. This was the reason Cho Chang and Ron had been jealous of them.
Then there was Hermione's reaction to Ron and Lavender dating, He can understand jealousy, but her attacking Ron and sniping at Harry was a tad overboard. Not to mention her distancing from Harry because of a potions book. He can easily deduce that Hermione loved Harry, but was actively trying to distance herself from him.
She might have decided after 5th year that she didn't want to be with Harry, There could be several reasons for it. It could be because Harry's chance of living through the war was not guaranteed, or it could be because she didn't think she deserved Harry, or it could even be that she couldn't fathom that Harry could have affection for her. Maybe it was a combination of all three, but it didn't matter, the result was that she went with the safe and easy choice.
So, Harry decided to shelve his feelings for her, at least at the time. She was severely deliciously punished by him, in the tent after Ron had bailed on them. He was pretty sure that the only reason she was with Ron right now was because her emotions were all over the place, and she had decided to focus all her attention on the war instead of her relationship with Ron and Harry.
The next on his list for girls to date was Daphne Greengrass, He had become fond of her and she had become a dear friend of his. She was beautiful, elegant, and didn't take shit from him. The stability she brought him was a welcome change from his usual acquaintances. He could also see that she held affection for him, it was not anything that could be seen easily. But he could easily pick them up, the attention she gave to him was different than she gave to her other friends. Her eyes always lit up when he talked with her, he had more than occasion seen her following him with her eyes when she thought he wasn't looking. Not to mention, the amount of care she gave him after Cedric and Sirius' death was easy enough proof
The problem was she was a Slytherin, Oh it didn't matter to him which house one was in. But it matters to everyone else, which is a big problem during the climate of Wizarding Britain. Voldemort and his followers would surely target whoever he was close to and he couldn't give her any protection in the Slytherin house. He wouldn't be able to help her if something happened to her when she was not with him, Hogwarts was not a safe place regardless of what its reputation touted.
She is a good option to pursue now, but at that time, a relationship between them was simply not feasible. He was already feeling angry and hurt, over Hermione pursuing Ron, and the affection and fondness he held for Daphne didn't allow him to endanger her. So, he went after the third-best choice, Ginny Weasley- a willing, easy, and best option for a short-term relationship.
His mind replayed through all the interactions he had with Hermione and Daphne, looking back he could see what kind of girls he wanted for his future. Their fierceness in facing the impossible, their inquisitive nature about anything and everything, and the smartness they displayed to tackle any objective. He could easily see, that he fancied women who reminded him of the best qualities of his mother- strong women who didn't shy away from taking a stand for what they believed in. When the whole world tells you to move, it's your job to plant yourself like a tree by the river of truth, and say "No, you move". He could vividly remember reading the line said by Captain America when he was a small, and scrawny kid who was treated like dirt. He had always associated with Cap and strived to live like him.
In the end, he decided that he would give Hermione another chance. He will see what her decision will be, regarding their relationship, when he'll be back from his long vacation. If she doesn't get her head out of her arse then it's her fault for missing out on something good. Harry decided, he would then start to pursue Daphne actively, which, to be frank, he was anticipating a lot.