u/CormundCrowlover

Stannis wants to knit the realm together, including the wildlings and marriages is a good way of doing it. We see Jon doing exactly that with Alys Karstark and Sigorn Thenn, though the main intention with this marriage may not have been this -I can't recall if we've ever been given his primary reason- he is well aware of this would help achieving it considering he sends Gerrick Kingsblood's daughters to Selyse for marriage.

>Red-bearded Gerrick Kingsblood brought three daughters. "They will make fine wives, and give their husbands strong sons of royal blood," he boasted. "Like their father, they are descended from Raymun Redbeard, who was King-Beyond-the-Wall." Blood meant little and less amongst the free folk, Jon knew. Ygritte had taught him that. Gerrick's daughters shared her same flame-red hair, though hers had been a tangle of curls and theirs hung long and straight. Kissed by fire. "Three princesses, each lovelier than the last," he told their father. "I will see that they are presented to the queen." Selyse Baratheon would take to these three better than she had to Val, he suspected; they were younger and considerably more cowed. Sweet enough to look at them, though their father seems a fool.
"A northern maid and a wildling warrior, bound together by the Lord of Light." Ser Axell Florent slipped into Lady Alys's vacant seat. "Her Grace approves. I am close to her, my lord, so I know her mind. King Stannis will approve as well."

Selyse also does this, marrying Gerrick’s daughters to her uncle and wanting to marry Val to Ser Patrek

>"Gerrick has graciously agreed to give the hand of his eldest daughter to my beloved Axell, to be united by the Lord of Light in holy wedlock," Queen Selyse said. "His other girls shall wed at the same time—the second daughter with Ser Brus Buckler and the youngest with Ser Malegorn of Redpool."

"Sers." Jon inclined his head to the knights in question. "May you find happiness with your betrothed."

"Under the sea, men marry fishes." Patchface did a little dance step, jingling his bells. "They do, they do, they do."

Queen Selyse sniffed again. "Four marriages can be made as simply as three. It is past time that this woman Val was settled, Lord Snow. I have decided that she shall wed my good and leal knight, Ser Patrek of King's Mountain."

"Has Val been told, Your Grace?" asked Jon. "Amongst the free folk, when a man desires a woman, he steals her, and thus proves his strength, his cunning, and his courage. The suitor risks a savage beating if he is caught by the woman's kin, and worse than that if she herself finds him unworthy."

One would expect Stannis to have thought of doing so as well, Axell Florent certainly thinks that Stannis would give the Stannis' nod of approval^(TM) to the marriage of Alys and Sigorn.

>"A northern maid and a wildling warrior, bound together by the Lord of Light." Ser Axell Florent slipped into Lady Alys's vacant seat. "Her Grace approves. I am close to her, my lord, so I know her mind. King Stannis will approve as well."

And in fact he did think of it, he tries to marry Val to Jon as part of a once in a lifetime package deal WWW: Winterfell + Wildling Wife

>"Whilst your brothers have been struggling to decide who shall lead them, I have been speaking with this Mance Rayder." He ground his teeth. "A stubborn man, that one, and prideful. He will leave me no choice but to give him to the flames. But we took other captives as well, other leaders. The one who calls himself the Lord of Bones, some of their clan chiefs, the new Magnar of Thenn. Your brothers will not like it, no more than your father's lords, but I mean to allow the wildlings through the Wall . . . those who will swear me their fealty, pledge to keep the king's peace and the king's laws, and take the Lord of Light as their god. Even the giants, if those great knees of theirs can bend. I will settle them on the Gift, once I have wrested it away from your new Lord Commander. When the cold winds rise, we shall live or die together. It is time we made alliance against our common foe." He looked at Jon. "Would you agree?"
"My father dreamed of resettling the Gift," Jon admitted. "He and my uncle Benjen used to talk of it." He never thought of settling it with wildlings, though . . . but he never rode with wildlings, either. He did not fool himself; the free folk would make for unruly subjects and dangerous neighbors. Yet when he weighed Ygritte's red hair against the cold blue eyes of the wights, the choice was easy. "I agree."
"Good," King Stannis said, "for the surest way to seal a new alliance is with a marriage. I mean to wed my Lord of Winterfell to this wildling princess."
Perhaps Jon had ridden with the free folk too long; he could not help but laugh. "Your Grace," he said, "captive or no, if you think you can just give Val to me, I fear you have a deal to learn about wildling women. Whoever weds her had best be prepared to climb in her tower window and carry her off at swordpoint ..."
"Whoever?" Stannis gave him a measuring look. "Does this mean you will not wed the girl? I warn you, she is part of the price you must pay, if you want your father's name and your father's castle. This match is necessary, to help assure the loyalty of our new subjects. Are you refusing me, Jon Snow?"

When that fails he considers Wyman Manderly in a later chapter

>"Lord Too-Fat-to-Sit-a-Horse." The letter that Lord Wyman Manderly had sent back from White Harbor had spoken of his age and infirmity, and little more. Stannis had commanded Jon not to speak of that one either.
"Perhaps his lordship would fancy a wildling wife," said Lady Melisandre. "Is this fat man married, Lord Snow?"
"His lady wife is long dead. Lord Wyman has two grown sons, and grandchildren by the elder. And he is too fat to sit a horse, thirty stone at least. Val would never have him."

Then in a later chapter he teases Jon with the possibility of Justin Massey and Richard Horpe getting Winterfell and therefore Val as well, offers him the WWW deal once again and when Jon refuses once more, he declares that his intention is to give Winterfell to Arnolf and though never outright stated, most likely Val as well, all within the same conversation.

>All of you did not seem to include Lady Melisandre. The king's red shadow. Stannis called to Devan for more lemon water. When his cup was filled the king drank, and said, "Horpe and Massey aspire to your father's seat. Massey wants the wildling princess too. He once served my brother Robert as squire and acquired his appetite for female flesh. Horpe will take Val to wife if I command it, but it is battle he lusts for. As a squire he dreamed of a white cloak, but Cersei Lannister spoke against him and Robert passed him over. Perhaps rightly. Ser Richard is too fond of killing. Which would you have as Lord of Winterfell, Snow? The smiler or the slayer?" 
"I have heard all I need to hear of Lady Lannister and her claim." The king set the cup aside. "You could bring the north to me. Your father's bannermen would rally to the son of Eddard Stark. Even Lord Too-Fat-to-Sit-a-Horse. White Harbor would give me a ready source of supply and a secure base to which I could retreat at need. It is not too late to amend your folly, Snow. Take a knee and swear that bastard sword to me, and rise as Jon Stark, Lord of Winterfell and Warden of the North."
How many times will he make me say it? "My sword is sworn to the Night's Watch."
Stannis looked disgusted. "Your father was a stubborn man as well. Honor, he called it. Well, honor has its costs, as Lord Eddard learned to his sorrow. If it gives you any solace, Horpe and Massey are doomed to disappointment. I am more inclined to bestow Winterfell upon Arnolf Karstark. A good northman."

He also says that once(if) he saves Arya, he'll find her a better match and in that same chapter Jon thinks how important it is that Stannis should act swiftly due to the diversity of his army.

>The Night's Watch was sworn to take no side in the quarrels and conflicts of the realm. Nonetheless, Jon Snow could not help but feel a certain satisfaction. He read on.
… more northmen coming in as word spreads of our victory. Fisherfolk, freeriders, hillmen, crofters from the deep of the wolfswood and villagers who fled their homes along the stony shore to escape the ironmen, survivors from the battle outside the gates of Winterfell, men once sworn to the Hornwoods, the Cerwyns, and the Tallharts. We are five thousand strong as I write, our numbers swelling every day. And word has come to us that Roose Bolton moves toward Winterfell with all his power, there to wed his bastard to your half sister. He must not be allowed to restore the castle to its former strength. We march against him. Arnolf Karstark and Mors Umber will join us. I will save your sister if I can, and find a better match for her than Ramsay Snow. You and your brothers must hold the Wall until I can return.
...
He wondered how many men old Crowfood would bring to the fray, and how many swords Arnolf Karstark would be able to conjure up. Half the Umbers would be across the field with Whoresbane, fighting beneath the flayed man of the Dreadfort, and the greater part of the strength of both houses had gone south with Robb, never to return. Even ruined, Winterfell itself would confer a considerable advantage on whoever held it. Robert Baratheon would have seen that at once and moved swiftly to secure the castle, with the forced marches and midnight rides for which he had been famous. Would his brother be as bold?
Not likely. Stannis was a deliberate commander, and his host was a half-digested stew of clansmen, southron knights, king's men and queen's men, salted with a few northern lords. He should move on Winterfell swiftly, or not at all, Jon thought. It was not his place to advise the king, but …

Each proving that Stannis is well aware of the importance of marriages in accomplishing his goal of knitting his realm of Wildlings, Northman and Southron together as much as he can.

So this begs the question, why did he not arrange any marriages with the hill clansmen whose daughters he was to praise the beauty of?

>"Ask, I said, not beg." Jon pulled back his hand. "It is no good sending messages. Your Grace will need to go to them yourself. Eat their bread and salt, drink their ale, listen to their pipers, praise the beauty of their daughters and the courage of their sons, and you'll have their swords. The clans have not seen a king since Torrhen Stark bent his knee. Your coming does them honor. Command them to fight for you, and they will look at one another and say, 'Who is this man? He is no king of mine.' "
"How many clans are you speaking of?"
...
"These mountain lords will not hinder my passage?"
"Only with feasts. Each will try to outdo the others with his hospitality. My lord father said he never ate half so well as when visiting the clans."
"For three thousand men, I suppose I can endure some pipes and porridge," the king said, though his tone begrudged even that.

Were their porridges so unendurable compared to the magnificence of the meals of Three Finger Hobb's whose cooking is so good he is a worthy candidate for being a Lord Commander? Is that why he wrote them off from the marriage list?

>Stannis ground his teeth. "It is not my wish to tamper with your rights and traditions. As to royal guidance, Janos, if you mean that I ought to tell your brothers to choose you, have the courage to say so."
That took Lord Janos aback. He smiled uncertainly and began to sweat, but Bowen Marsh beside him said, "Who better to command the black cloaks than a man who once commanded the gold, sire?"
"Any of you, I would think. Even the cook." The look the king gave Slynt was cold. "Janos was hardly the first gold cloak ever to take a bribe, I grant you, but he may have been the first commander to fatten his purse by selling places and promotions. By the end he must have had half the officers in the City Watch paying him part of their wages. Isn't that so, Janos?"

"The cook. That wonderful cook. Here at the end of the world everything was cold, barren, and lifeless, except for the meal hall..."

But in all seriousness, why were there no marriages with the Hill Clans?