It's hard to pick one part of Jon's narrative arc that I enjoy the most because he's a dynamic character who evolves quite a bit. However, one part of Jon that I appreciate is that as he grows, the people he chooses to admire as his own personal heroes do as well.
When Jon had been a boy at Winterfell, his hero had been the Young Dragon, the boy king who had conquered Dorne at the age of fourteen. Despite his bastard birth, or perhaps because of it, Jon Snow had dreamed of leading men to glory just as King Daeron had, of growing up to be a conqueror. Now he was a man grown and the Wall was his, yet all he had were doubts. He could not even seem to conquer those.
-ADWD, Jon VII
When Jon had been Bran's age, he had dreamed of doing great deeds, as boys always did. The details of his feats changed with every dreaming, but quite often he imagined saving his father's life. Afterward Lord Eddard would declare that Jon had proved himself a true Stark, and place Ice in his hand. Even then he had known it was only a child's folly; no bastard could ever hope to wield a father's sword.
-AGOT, Jon VIII
Jon's first ideas of heroism/great men come hand in hand with the certainty that he will never be one. He denies himself hope; he denies himself even childhood. Maybe that's because he doesn't feel like he's allowed to have those things.
"I am almost a man grown," Jon protested. "I will turn fifteen on my next name day, and Maester Luwin says bastards grow up faster than other children."
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He had thought on it long and hard, lying abed at night while his brothers slept around him. Robb would someday inherit Winterfell, would command great armies as the Warden of the North. Bran and Rickon would be Robb's bannermen and rule holdfasts in his name. His sisters Arya and Sansa would marry the heirs of other great houses and go south as mistress of castles of their own. But what place could a bastard hope to earn?
-AGOT, Jon I
[That isn't how the adults around him see it, just Jon's perspective - "And even a bastard may rise high in the Night's Watch," Ned reflected. Still, his voice was troubled. "Jon is so young. If he asked this when he was a man grown, that would be one thing, but a boy of fourteen…" (AGOT, Catelyn II)]
But his admiration of warrior princes and kings muddles quickly.
Jon was still not certain how he felt about it. Robb a king? The brother he'd played with, fought with, shared his first cup of wine with? But not mother's milk, no. So now Robb will sip summerwine from jeweled goblets, while I'm kneeling beside some stream sucking snowmelt from cupped hands. "Robb will make a good king," he said loyally.
"Will he now?" The smith eyed him frankly. "I hope that's so, boy, but once I might have said the same of Robert."
-ACOK, Jon I
Specifically Jon's relationship with the King he meets face to face, Mance, is a complex one - Mance is Ned Stark's enemy, a man who broke the vows Benjen and Jon swore, and he's in league with the North's ancient enemy. Besides that, he doesn't look much like a warrior.
"[Mance] was the best of us," said the Halfhand, "and the worst as well. Only fools like Thoren Smallwood despise the wildlings. They are as brave as we are, Jon. As strong, as quick, as clever. But they have no discipline. They name themselves the free folk, and each one thinks himself as good as a king and wiser than a maester. Mance was the same. He never learned how to obey."
"No more than me," said Jon quietly.
-ACOK, Jon VII
The singer rose to his feet. "I'm Mance Rayder," he said as he put aside the lute. "And you are Ned Stark's bastard, the Snow of Winterfell."
Stunned, Jon stood speechless for a moment
-ASOS, Jon I
Mance had spent years assembling this vast plodding host, talking to this clan mother and that magnar, winning one village with sweet words and another with a song and a third with the edge of his sword, making peace between Harma Dogshead and the Lord o' Bones, between the Hornfoots and the Nightrunners, between the walrus men of the Frozen Shore and the cannibal clans of the great ice rivers, hammering a hundred different daggers into one great spear, aimed at the heart of the Seven Kingdoms. He had no crown nor scepter, no robes of silk and velvet, but it was plain to Jon that Mance Rayder was a king in more than name.
-ASOS, Jon II
[Contrast to another man who doesn't "look like he should" yet Jon dislikes him. "The king was a great disappointment to Jon. His father had talked of him often: the peerless Robert Baratheon, demon of the Trident, the fiercest warrior of the realm, a giant among princes. Jon saw only a fat man, red-faced under his beard, sweating through his silks. He walked like a man half in his cups." (AGOT, Jon I)]
I'm not quoting this out but I think it's artful that GRRM puts Jon in Mance's camp right before Stannis comes to the Wall. Mance's host is impressive (an entire people) but it lacks discipline (Mance is all that holds them together). Stannis's army is small, but disciplined, and Stannis is as rigid as Mance was malleable to the unique needs of the wildling clans ("Let them keep their pride, and they will love you better." His Grace would not listen. He said, "It is swords I need from them, not kisses.") Jon never admires Stannis per se, actually he's more annoyed than awed even when Stannis offers him Winterfell and a Stark name.
Now, ADWD Jon Snow is someone who's been analyzed at length - he's harder and meaner than ASOS Jon. He's no longer able to compromise with the stakes so high, and in many ways he lacks his previous faith. If AGOT Jon didn't dare dream, ADWD Jon runs on nothing but dreams, holding together his patchwork peace in the same way that Mance did his, while running the Night's Watch with the brutal efficiency of Stannis Baratheon.
But those aren't Jon's heroes or role models...
This was pointless, Jon thought. Pointless, fruitless, hopeless. "Thank you for your counsel, my lords."
Satin helped them back into their cloaks. As they walked through the armory, Ghost sniffed at them, his tail upraised and bristling. My brothers. The Night's Watch needed leaders with the wisdom of Maester Aemon, the learning of Samwell Tarly, the courage of Qhorin Halfhand, the stubborn strength of the Old Bear, the compassion of Donal Noye. What it had instead was them.
-ADWD, Jon XIII
This is such a seminal Jon Snow quote.
Maester Aemon? Wise. Wisdom isn't about his education, it's about his perception and empathy. Maester Aemon is always the one to offer advice when AGOT-ASOS Jon is going through crises of identity as the brother-son-bastard of House Stark vs. being a man of the Night's Watch. Only Aemon knows what it means to have a King for a brother. Although he's not present for most of ADWD, Maester Aemon's words of kill the boy, let the man be born are what Jon clings to.
Sam Tarly isn't learned, he's learning. Sam Tarly dreams and reads and saves Gilly when Jon couldn't. There's a lot to say about how Sam represents humanity to Jon but for the point of this post, it's important to note that Jon admires him for it. Loves him.
Qhorin Halfhand, whose time with Jon was limited but a) in that time, he opened Jon's eyes to a new perspective on the wildlings, and b) was willing to sacrifice everything for his beliefs.
Donal Noye! This one is fantastic because Donal Noye is formative during Jon's time in the Watch. He's not a flashy ranger (Ben Stark isn't even included in Jon's top five brothers of the Night's Watch list! RIP bozo jk Jon does call him one of the best men of the Watch in ADWD Jon V), he always phrases things in the worst possible way (you're a bastard and a bully; The moles all went in terror of him, and rightfully so, since he was always threatening to rip their heads off), he's just the quasi-leader of Castle Black who holds Jon down with his only arm while Aemon cauterizes his wound.
And what Jon admires in him is his compassion.
It's probably arguable that Jon names these people as a way of comforting himself, because ADWD Jon doesn't particularly like his own actions. He weaponizes his bastardry against himself and he's consumed with doubts.
But there's an empathic reading too, that these are all people on the margins of the social order, and they're all people who enriched Jon's life personally. They taught him hard lessons and happy ones, and whoever he is, whether Jon or Lord Snow, a rebel and a turncloak, aye, and a bastard and a warg as well - he chooses to rely on their strength and memory to guide him. Jon Snow thinks better of himself for having known these people, and so his heroes morph from warrior princes and doers-of-great-deeds to those who are able to improve the lives of their friends and brothers even in impossible situations.
ADWD Jon Snow is incomplete and often in pain, but he's not stagnant. In fact for once he's allowing himself imagine a future of his making, in no small part because he's seen these men do the same.
"Every man who walks the earth casts a shadow on the world. Some are thin and weak, others long and dark. You should look behind you, Lord Snow. The moon has kissed you and etched your shadow upon the ice twenty feet tall."
-ADWD, Jon VI
