"Ain't No Sunshine": Nathan's reaction to Audrey's kiss.
And the entire episode "The Hand You're Dealt" (the pyro one), where Nathan is constantly finding excuses to touch Audrey—hand shakes, high fives, and so on. It would be creepy anywhere else, but in context its adorable since he can't feelanythingbut Audrey.
Also counts as something of a moment of funny since both in-universe and out, every one seems to notice his very odd behavior but they just don't comment.
Taking in a stray cat.
The Ending of the 10 plagues episode with the happy baby and the shadow rabbit.
"Fear and Loathing": Nathan giving up his ability to feel to allow Jackie to be rid of her much more cumbersome trouble.
Nathan: (to Jackie) You have beautiful eyes.
"Love Machine": Audrey II loses all her memories, and Audrey soothes her. Later, Audrey adds the wind chimes that Audrey II had suggested even though she earlier thought it was stupid.
Audrey: Do you know who you are?
Audrey II: Yes. I am... I... am... Oh, god, I...
Audrey: It's okay. I'll tell you. Your name is Audrey Parker. You like—you like matinees in empty theaters. You hate runny eggs.
Audrey II: What else?
Audrey: You're an FBI agent. You became an FBI agent because you felt that if you could help people, help people in trouble, that you could—that you could connect.
Audrey II: I'm sorry, I don't remember any of that.
Audrey: That's okay. That's okay, because I do.
Audrey II: How?
Audrey: (tears flowing) You're my friend. We're like sisters.
Also in that episode The mechanic whose machines are coming to life to kill anyone who tries to get him to leave town, being forced to choose the machines due to the fact that they would kill the woman he loves if he didn't stay with them and let her move out of town alone.
"Business As Usual": Nathan giving Audrey Lucy's address, followed by Audrey promising she will come back and then finally kissing Nathan on the lips.
Lucy Ripley's reaction when Audrey arrives. From Lucy's point of view, she's meeting a beloved friend she has not seen in 27 years. Audrey's past incarnation asked her to wait until she came back. She waited.
"Sins of the Fathers": Duke, when faced with the ghosts of his father and the Reverend telling him not to listen to Audrey, that she's a liar, quietly replies, "No. She's my friend."
"Silent Night": Audrey getting Nathan and Duke the present they wanted.
"Over My Head":
Duke saving Daphne.
Jordan McKee explains that her Trouble causes anyone who touches her skin to feel unbearable pain and she has no control over it. Without hesitation, Nathan grabs her hand, his Feel No Pain Trouble making him immune. She practically cries Tears of Joy.
Duke says that while Audrey disappearing every 27 years is a bad thing, he's glad because it allowed him to meet her.
Audrey defying Lady Justice and Lynette by telling them that Duke is a true hero despite being a criminal.
In 1955, Nathan runs into a child version of his father, Garland Wuornos. The boy asks him if he can be a policeman when he grows up, and Nathan assures him that he can.
In the Bad Future, Audrey finds Garland Wuornos is alive. Garland believes her story, and is willing to help her try to get Haven back to normal, even though he is dead in the true timeline, just because in the original timeline, Nathan lived.
Sarah showing Stuart a picture of himself in the future, old and with a family, to help him get over his fear that he's going to die.
In "Burned," any scene with Ginger and Duke is just so freaking adorable. Especially when he tells her about his little girl, from "Ball and Chain" whom most have forgotten about. The second time in particular since Ginger suggests he and Jean can come visit them. Crosses over into Tearjerker since Duke, knowing that he can never see Jean, can only look away with a pained look in his eye.
In "Last Goodbyes," both Duke and Nathan's interrogations and memories of Audrey to prove they weren't the skinwalker were incredibly sweet and comforting. Both of their faces were just full of "Awww..."
Audrey and Nathan dancing to "On Bended Knee" by BoyzIIMen. Perfect.
Jeanine confessing to Robert, who used to be the class geek, that she had always loved him and was too shy to admit it, proving it by showing she remembers everything about him.
"Fallout": Nathan hugging Duke after Duke was missing for six months. Nathan has spent three seasons sparring with Duke, and was particularly hostile in the season preceding this episode, but for once there's not a hint of reserve or antagonism; he's just honestly, openly overjoyed that Duke is back.
"Lay Me Down": Nathan tells Audrey, "I don't care who you are or what you are. I love you."