Contrary to popular sentiment that views ambition as an inherently negative character trait, it is not bad or harmful in and of itself. It’s only when people prioritize it above all else that it becomes bad; when they start stepping on others or putting them into dangerous or unwanted situation or denying them even their governance over their own bodies that it becomes harmful. To this effect, Rickard Stark’s problem wasn’t that he had ambitions for his children or that he looked to the south for alliance, it was that he forced Lyanna into a betrothal that she did not want and a marriage that would have made her miserable (and probably abused). Hoster Tully’s problem was not that he wanted a high marriage for his daughter, it was that he believed that the advancement of his House and his reputation was worth violating her body autonomy and putting her through the physical and emotional trauma of a forced abortion.
In that vein, Ned’s character is a very important factor in this conversation. This AU changes his trauma responses which is what drives a lot of his decisions in OTL; Ned’s desire to be left in peace in the North and his ill feelings towards the south was born out of his trauma during the rebellion, so was his inclination to keep his family around him and refusing to foster out any of his children after he lost his father and siblings in short order so I gotta say it’s a little hard to imagine a Ned who has “southron ambitions” since it was those ambitions that ended with almost all of his family dying on him before he was even 20. Why do I care about this when I could just rattle some options for fostering and marriage alliances? Because Ned’s overall personality is an integral part of his decision-making process when it comes to his politics. For example, would he be more open to a position in King’s Landing in this scenario? Would he have an eye on Robert’s children as potential matches for his children? Note that an ambitious individual with Ned’s circumstances could have capitalized on his connections to the new ruling regime post-Robert’s Rebellion, and gotten honors and high offices lavished on him by his eager royal foster brother, which would have landed him in King’s Landing with a seat on the small council and great sway in Robert’s government. But Ned didn’t because of a mix of a psychological wish to leave the south after what happened to his family, and a necessity for keeping his distance from Robert because of Jon. An ambitious individual would have actively pursued a match between Sansa and the dynastically excellent Joffrey, but Ned was wary and grudgingly accepting at first, then went to the extent of talking about breaking the betrothal before he guessed the truth about Joffrey’s parentage. Ned was not your average feudal lord who saw his children as marital pawns and instruments of alliances first, and whose focus in a betrothal was the amount of power it could bring him above the well-being of his children.
That is all to say that it’s a bit more complicated than just figuring out where Ned would foster his children and who he’d marry them to, because I have to find a balance between what southron ambitions means to Ned and the changes this bring as he perhaps seeks to be more involved in politics to the south, and the fact that this was a man who defied the social norms of his time by caring about the character of the people marrying his daughters and not wanting his children to be betrothed young. Ned was a man who cared more about his children’s well-being than he did any political gain. Those are elements that I can’t see going anywhere, otherwise Ned would lose the core of who he is as a person and wouldn’t be Ned at all.
Following that, I don’t think there is a strong possibility for Ned to foster out his children, even if he has political interests dependent on that fostering. For one, while fostering is a very useful method of building alliances, Ned could easily follow in the footsteps of his father-in-law and rely on marital alliances instead. Indeed, I think the chances of this are high, both because of Ned’s desire to keep his children around him in Winterfell and because of Jon Snow. That Jon gets to grow up in Winterfell under Ned’s tutelage and with his children is important to Ned, but it’s not something he could swing if he is to attempt to foster away his children with Catelyn. Keep in mind that Catelyn consistently tried to get Jon sent away so if Ned was to foster out any of her children, she wouldn’t have budged in demanding that Jon be sent away as well. After all, Ned couldn’t very well demand that Jon stay but send Catelyn’s children away. It’d be a major point of criticism and wonder if the Lord of Winterfell scatters his trueborn children but keeps his bastard son by his side, which would have serious political implications if Ned is seen to favor his bastard son over his trueborn one (and the Blackfyre rebellions were on Catelyn’s mind as it was.) So fostering is out unless Ned is prepared to send Jon away.
As for the matter of the betrothals, an eye towards the advancement of his House and Ned’s own personal priorities aren’t the only considerations here; he also needs to take into account the reaction of his bannermen when deciding on matches for his children. With the memory of the disastrous results of Lord Rickard’s own southron ambitions still in living memory, and given the fact that the Northern lords have been deprived of a Stark match from the previous generation, in addition to their natural dislike of the south, it is politically prudent for Ned to marry more than one child to the North to appease his bannermen and avoid unwanted discord in the North. Robb, in particular, is a lock-down for a Northern match, because (1) he is the heir and thus the greatest marital prize the Starks have to offer and so (2) his marriage to the North would go a long way in satisfying the Northmen more than any of his siblings, and (3) with a southron mother whom he favored in looks, marrying Robb to the south risks him being branded as “too-southron” in the eyes of his prickly future bannermen, a rather unfavorable image for the future Lord of Winterfell to have, especially in the presence of the Stark-looking, uber-Northern Jon Snow, or so Catelyn might figure. Of the possible matches, I’d say Wylla Manderly is the most likely choice. The Manderlys are the richest and most powerful Stark vassals which makes them the most impressive match within the North, which would fit Ned’s ambitions nicely in this scenario without being a too controversial match. The Manderlys may be Reacher expatriates, but they have been in the North for over a thousand years and have provided brides for House Stark twice before. The other potential brides within Robb’s age range are Meera Reed and Alys Karstark. The former might appeal personally to Ned considering his friendship with Howland, but an alliance with Greywater Watch offers little in terms of political power and I don’t know about Catelyn’s reaction since crannogmen aren’t exactly esteemed in the Seven Kingdoms or even in the North itself, though Ned’s personal regard for Howland would hold weight for her. Alys makes for a more traditional marriage partner for a Stark since Karstarks have been Stark brides thrice before, and we know that her father had an eye on this match since she and Robb were children. She also offers a seamless affirmation of Robb’s Northern roots due to her Stark blood.
As much as Robb is more likely to marry to the North, Sansa is almost certainly getting married to the south in this au. Unfortunately, Joffrey Baratheon is the most impressive dynastic match in Westeros so he is still the most likely choice. But here’s where possible changes might prevent that betrothal: if Ned is more involved in southern politics in this au in a way that brings him to King’s Landing if even occasionally, chances are he’d have some contact with Joffrey and be even more wary of a match with the crown prince than he was in OTL. Ned cared about the character of his daughters’ bridegrooms so if he has a better grasp on Joffrey’s personality before Robert suggests the match and he feels he has to accept it, he might try to broker another betrothal, though the chances of that are quite low since Robert suggests the match with Joffrey when Sansa was only eleven and Ned would not betroth her before that. Poor dear most likely still gets stuck with Joffrey. Who else would be suitable for Sansa? Hmm, one of her uncle’s future bannermen might be a good choice, if not especially advantageous since House Stark is already married to the Riverlands’ ruling family. But someone like Patrick Mallister remains a nice option. Fandom is quite fond of Willas Tyrell as a match for Sansa but while Willas is an impressive dynastic match, he is significantly older in a way that I don’t think Ned would want, not to mention that Ned didn’t have much (or any) relationship with Mace Tyrell. The heirs of the most prominent Vale families also fall under the too old umbrella. (And no, a match to Harry Hardyng can’t happen since it’d be a statement from Ned and Catelyn that they do not expect Robert Arryn to survive which is a poor message to send in normal circumstances but even more so in light of the familial connection between the Starks and Arryns. As for Robert Arryn, he is a bit on the younger side for Sansa.)
Arya, I can see go either way. A good dynastic match for her would be Robert Arryn. He is only a couple of years younger than her, and her cousin besides. If she is betrothed to Robert and Sansa to Joffrey, that would be quite the neat affirmation of the Tully-Stark-Baratheon-Arryn alliance. Downside is that if Ned witnesses Lysa’s deterioration and her encouragement of Robert’s dependency on her, which would be quite disturbing for him, he might not be too keen on the match. Robert is also very ill, which would raise concerns about his survival, or even his ability to father children in light of his parents’ fertility problems. But I can also see Ned marrying Arya to the North. She’d certainly prefer a match closer to her family rather than being sent south. Giving a Stark bride to a Northern house would also be a good idea since it’s been generations since a Stark bride was last married to the North (we have to go back to the generation of Lord Beron Stark, Rickard’s great grandfather to find a Stark bride who married to the North, though we do not know the marital fates of Beron’s daughters Alysanne and Berena. Still, even if we assume they married Northmen (probable), that still leaves a three-generation gap in which the only two available main-line Stark brides were married to a Royce and betrothed to a Baratheon respectively – and the two known non-main-line Stark ladies married a Stark (Ned’s mother Lyarra) and a Rogers from the Stormlands (his aunt Branda)). The two heirs within Arya’s age range are Cley Cerwyn and Jojen Reed, not as impressive of a dynastic match as an Arryn or even some of the other more powerful Northern Houses, but Cley has the advantage of proximity to Winterfell (only half a day’s ride away making them frequent visitors of Winterfell) which would certainly appeal to Arya, while Jojen has Howland’s friendship with Ned going for him, though sending her daughter to the swamps of the Neck would not go well with Catelyn, I reckon. Another choice that might be a middle ground between what Arya might prefer and what Catelyn and Ned want for their daughter is Brynden Blackwood, a match that wouldn’t be disliked by the Northern lords due to House Blackwood’s Northern origins and that might appeal to Arya for the shared cultural and religious origins.
Bran is another I see Ned and Cat planning on a southern match for given his desire to be a knight and fascination by chivalry and stories about knighthood. Known noble ladies in Bran’s age bracket are limited though so this is a bit hard. Myrcella Baratheon obviously, but a Northern second son isn’t an impressive match for a princess and Cersei is sure to object (and it definitely would not happen if SansaJoffrey is a go). Shireen Baratheon is a possibility as the heiress to Dragonstone, the daughter of the Master of Ships who Ned respects and the king’s niece, except Stannis resents Ned, Dragonstone isn’t the most bountiful seat (if still a definite improvement on the Northern holdfast Bran was promised), the relationship between Stannis and Robert is fraught, and why go for an alliance with Stannis if one is assured with Robert? Bethany Blackwood is another possibility that fits Bran’s shift towards the old gods, and would be received favorably by the Northmen as a Stark match. Jonos Bracken has daughters but 1) I hate that guy, 2) we don’t know how old his daughters are and 3) in a choice between Bracken and Blackwood, you bet everything that Ned would go for the old gods-worshipping, Northern-blooded Blackwoods who he counts as kin.
As for Rickon, who the hell knows. Lyanna Mormont is a fan favorite, but no matter how much I love the Mormont ladies, they are not good dynastic matches. House Mormont is impoverished and no one knows the identity of the father(s) of Maege’s girls, fathered by a bear as she claims. The kid’s age also means that possible brides for him probably hadn’t even been born yet when Ned was killed, and the only person within his age range that we know of is Erena Glover. So really, we all say Erena Glover because we don’t have any other choice in the North, much less the south. But to discuss Erena as match, it’s important to note House Glover is a masterly House, not a lordly one so not a lot of political advantage there. However, Rickon is the youngest of five so that allows for more leeway in picking his match than his older siblings, and it would not be the first time a Stark took a Glover to wife. On the upside, the Glovers have shown consistent unflinching loyalty to House Stark across multiple generations, and there is also a rebellion-forged personal connection between the two houses with Ethan Glover being the sole survivor of Brandon’s entourage and one of Ned’s companions that died trying to rescue Lyanna at the Tower of Joy.