"Niko, my cousin!" *hugs* Even though he's drunk at the time, Roman's joy at having cousin Niko in Liberty City is a pretty good moment to make you smile.
Roman comforting Niko after Niko kills or spares Darko Brevic.
The stranger quests, showing a lighter side to Niko (sometimes) involving rescuing a failing rapper being harassed by thugs, giving money to a drug-addled prostitute and taking her home, helping a recently divorced woman, stopping Anna Faustin's (Mikhail's daughter from way back at the beginning) new boyfriend from turning her into a whore, helping Ivan and Cherise, if you let them live, paying off some debts with newly reformed ex-drunkard Mel and getting old friend Hossan's money back from an employer.
More needs to be said about Marnie (the drug-addled prostitute). In her second mission you take her to the train station and give her some money for her journey home. Afterwards you get an email from her, telling you just how much you've changed her life. In a game where nearly everyone you meet you kill and end up in a little better situation then you left, it's one of the few genuinely bright spots.
Despite Kate getting killed in the "Revenge" ending, one of the phone calls that Niko receives during the end credits is from Roman, who says that Mallorie, his wife, is pregnant, and if it's a girl, they'll name her Kate. Happily contrasted with the "Deal" ending, where not only does Roman die, leaving Mallorie a child without a father to raise, but Kate breaks up with Niko for being a greedy jerkass.
Out of all the snippets of dialogue that accompany the much-maligned Friendship Activities, one really stands out as the most heartwarming of them all: After several friendship activities (and subsequent conversations) wherein they criticize each other's lifestyles, Roman and Niko finally tell each other of how much they respect the other. Niko admits that he admires Roman for being so optimistic even in the darkest of circumstances, while Roman praises Niko for his integrity and firmness in his beliefs, and they conclude with both of them wishing they could be like the other. It's one of the few moments in the game that unquestionably succeed at humanizing Niko.
Bernie Crane's whole character is heartwarming when you think about it: he's seen all the horrors that Niko has, yet he managed to move on and live a very happy life. He managed to start over and move on from the past, something Niko could never do, sadly. That Niko accepts his old friend's lifestyle without judgment fairly quickly is touching, as well. In fact, the mission where you give a homophobic bully the beatdown he deserves for Bernie can be a crowning moment of awesome, heartwarming and funny all rolled into one.
The mission where Nico rescues Roman from kidnappers doubles as a Crowning Moment of Awesome. Niko completely LOSES it during the mission and his normally stoic demeanor is completely dropped for a combination of rage and panic. The visible sense of relief he has at the end makes it all the more worth it.
Befriending Dwayne Forge. His past rivals Niko's in having to be a criminal purely for survival, (hence why Niko invokes Not So Different,) his time in jail's made him a Stranger in a Familiar Land with his friends and girl having ditched him despite all he's done for them, namely Cherise, leaving him borderline-suicidal and the game makes you feel like an utterbastard if you kill him in "The Holland Play" where gameplay-wise it's embarrassingly easy and only pays out money you could make in a matter of missions anyway, while storyline-wise Dwayne's hatred of you is palpable as is Playboy X blaming you despite it being on his orders, so Story Branch Favoritism is in full effect, but do the opposite and his gratitude is just as palpable both in gameplay in sending actually helpful Mooks to back you up in fights and giving you the 2nd-best safehouse in the game that includes the Claude outfit as well as narratively in him opening up to you and that your faith in him was well worth it. Good Feels Good, indeed.