Hell, Data in general throughout the whole damn movie. When he isn't annoying the heck out of you he's generally tugging the heartstrings.
Let's add him gently cradling Deanna during the crash, particularly considering his earlier freezing up when Geordi was in danger.
Speaking of which, after Lursa and B'Tor demand a hostage exchange in return for freeing Geordi, Data immediately volunteers before Picard says otherwise. And Geordi doesn't begrudge Data in the slightest.
Picard seeing René in the Nexus. Just the Nexus in general, really. Kirk got shortchanged with the constant shifting, but for one brief moment, Picard had everything he wanted. At the same time, he's willing to give it up, because his crew needs him.
It's a kind of a cross between heartwarming and funny.
Picard: Good luck Captain. Kirk: Call me Jim.
"It's the least I could do... for the captain of the Enterprise. It was... Fun."
The conversation at the end between Riker and Picard as they bid goodbye to the Enterprise-D.
Picard: Somehow I doubt this will be the last ship to carry the name Enterprise.
There is an "echo" of Soran in the Nexus, so at least a tiny bit of him is happy in the Nexus.
"It wouldn't be the Enterprise without a Sulu at the helm." Given the bad blood between Takei and Shatner, that line almost comes across as a peace offering.
Picard and Kirk meeting in general. Sure this movie has it's ups and downs, but his meeting of the Captain causes so much awe in him that the first thing he ever does, is say Kirk's name in a disbelief whisper. Extra heartwarming on Kirk's half though, as despite not knowing Picard save for the fact that he is a stranger in a Starfleet uniform, yet he is kind enough to offer him breakfast and invite him to his house. Even Picard is obliged enough to help him cook. Makes you wonder what meeting Kirk would be like in real life when he's on Shore Leave.
Of all the reasons Kirk could give to remain captain of the Enterprise (and indeed there are many), his true reason shines above them all.
"[...] because while you're there, you can make a difference."