An easy to miss moment in Vice City happens in the cutscene when you start the first mission after buying the Print Works. Tommy Vercetti, the ruthless 'Butcher of Harwood', is looking over the printing machines in the property he'd just bought... and he starts reminiscing about the evenings in his childhood, cleaning the rollers with his father, even admitting that he'd planned on following in his father's footsteps before he ended up in the gangster lifestyle. He even wants to use the print works for something honest like printing a newspaper or a magazine rather than selling the machinery for scrap and repurposing the property, as a little nod to his father. Of course, old man Kelly convinces him to turn it into a counterfeiting operation instead, but it's still a remarkably humanising moment for such a brutal character.
Also, in the penultimate mission, "Cap the Collector", Sonny Forelli's thugs have assaulted Old Man Kelly at the Print Works in their attempt to collect "Sonny's share". Even before learning Sonny was responsible, Tommy is righteously pissed.
Old Man Kelly: Tommy, rip that guy a new asshole for me!
Tommy:I'm gonna rip him two!
Tommy generally doesn't trust anyone throughout the game, but his friendship with Colonel Juan Garcia Cortez is genuine and honestly heartfelt. When Cortez calls Tommy to tell him he needs to flee town and ask for his help, Tommy is clearly happy to help. After you've completed the mission and Tommy is saying goodbye to Cortez, the man even asks Tommy to look after his daughter Mercedes for him while he's gone and Tommy agrees. "I think she could look after herself, but sure, I'll keep an eye out."
And at the end, the only guy in town left standing to profit from Tommy taking over Vice City? Ken Rosenberg. The very first ally you get in the city. There's even a CasablancaShout-Out!
There's the cut scene after Tommy helps Cortez take out some enemies. Cortez gives Tommy a boat. Tommy replies "Thank you, colonel" and he sounds noticeably moved.
When Lance calls Tommy a few times and is noticeably struggling from his inferiority complex and narcotics addiction, Tommy speaks gently to him and tells him to take a few days off. He knows that Lance is a liability, but he still looks out for him.
It's also noteworthy that he rescues Lance from being tortured by Diaz's men. This effectively ruined his relationship with Diaz (not a wise person to get on the wrong side of) and saved Lance at no gain to himself. Tommy also helps out Phil when he blows his arm off, which was nice given that he no longer had much use for Phil after the bank heist.
Lance is trying to avenge Vic's death. Given how strained their relationship was at times, it's nice to see that he truly cared for his big brother.