The end of the first arc where, after Brody has learned to accept his new life and training from Kagemura, he cleans himself up and goes to meet with Nicole—not in a desperate attempt to get her back, but just to let them end on a better note than before and give himself closure. It goes perfectly, and they're both smiling by the end of it. It may be mitigated by his vision of her murder later, but it was a sweet moment nonetheless.
When Brody reveals his powers and mission to stop the Penny Murderer to Gabe, rather than call him crazy like every other person that Brody shared the story with, Gabe gives him a chance and actually helps him with his investigation (at great risk to himself, at that.)
The scene when Brody visits Talia's mother, the mother of the first Penny Murderer victim. Talia warns him not to, fearing that all he'll do is ruin her fragile sanity by dredging up the past, but when he tells the woman that he's been seeing Talia's ghost, she reveals that she has repeatedly felt Talia's presence and hid it from everyone because she feared they'd think she was still insane. Brody reassures her that if she felt Talia's presence, it's because Talia was actually there visiting her.
On a broader note, there are several occasions where Brody visiting the families and friends of the murdered girls leads to him reassuring them that he will bring the murderer to justice, a reassurance the actual police couldn't give.
It's very bittersweet, but when Talia comes back to Brody to say thanks for everything he did, and although she refuses to apologize, she admits that she put him through a lot, and that she still wants to be his friend. Brody gives her a lukewarm reception, but he does explain to her why the Penny Murderer picked her to die, and a little later Talia tries to comfort him on how things turned out by telling him he's a hero for what he did.
The final note of the series, which has another conversation over coffee between Brody and Nicole, who finally understands everything that Brody had been trying to do for her (and Brody, for his part, forgives her for what she did to him in turn.) It's implied that they get back together in the end.
Brody: There are a lot of days in my life I honestly wish had never happened. There are other days, though, that I wouldn't trade for anything on earth. Like that day, for example. ...And all the days that followed it.