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He never stops looking. All through his tenth self's life, and even beyond, he never stops looking for ways to fix her, to give her back the memories he had taken so cruelly from her. He can't stop, because she deserves so much better than what she got, and anyway, she had promised him forever, hadn't she?
After his regeneration, he finds a new companion, because that's what she would have wanted him to do. Her voice from that Christmas a lifetime ago echoes through his mind. Just promise me one thing: find someone.
And she was right, he did need someone. Someone to stop him, to pull him back when he gets too close to the edge, and someone to push him forward when he's too tired to keep going. Someone to remind him that life is worth living, because as he said once, there’s always something worth living for. He just…forgets, sometimes.
So he did find someone else. Two someones, actually. Amy Pond, a redhead - just like her - who is young and in love and full of life. And Rory - sensible, dependable Rory - who would be quite content to live his life with his feet firmly on the ground, but travels with him anyway because that's just the kind of love he has for Amy.
So he keeps traveling, saving worlds and defeating monsters, and with his two companions, learns to truly enjoy the wonders of the universe again. Throughout the adventures, Amy takes his hands and calls him her Raggedy Doctor. He likes the nickname, because it fits this body so very well, but sometimes, just sometimes, he wishes that a different redhead is calling him her Spaceman instead. And when Amy calls him her best friend, he smiles at her but never says it back; for him, that position is filled, and he wouldn't want it any other way.
And when the both of them leave, as all his companions must in the end, he bids them goodbye and wishes them a happy life. And he carries on, finds other companions and has other adventures. But he never, ever, forgets Donna Noble, for she had become his conscience, a little voice in the back of his head that tells him off in no uncertain terms when he's being a prat. And he never stops looking, either, because she will always be his best friend, and no amount of time and space can change that simple fact.