Alistair has many lovely moments, but the rose is probably the best. I wasn't expecting it the first time, either, so it seemed even more special somehow. I've done playthroughs with all the options in DAO but that is still my favourite.
(Although sad little shout-out to Nelaros, the ill-fated fiance of the female city elf. He made her a ring, promised to make her happy, and tried to rescue her, all without actually knowing her. That was a relationship that could have been so different and so lovely.)
DAII: Fenris is an angsty bother sometimes, but his apology for having left Hawke hanging years before is something really very sweet.
DAI: There is a moment toward the end of the story when the Inquisitor might stumble in on Cullen praying that is lovely. Later, in Trespasser, when the Anchor is heading toward meltdown and the Inquisitor says look, I just don't know how much time I have. Cullen's face is so earnest and sad right then I haven't the words.
And Dorian has these little occasional moments of vulnerability where you remember that he's basically a runaway kid, and younger than he looks.