As soon as Ned reached Eeyrie he started penning letters. First one to Father informing him about the promised aid from the Crown to Nights Watch, then enquiring about well being of his siblings, present status of Winterfells larders and treasury and progress on the reconstruction of the Moat and if any betrothals were arranged yet. Second one to Brandon inquiring on the status of his spy ring. And the third one to Rhaegar informing the Prince of his safe return to Eeyrie and asking after his health. Rhaegar and Ned decided that the Prince shouldn't write or recieve any encoded letters while the Prince was at Kingslanding, as it would not serve to have the spies at the Court to find out that the Prince is writing and receiving secret communique, oly after the Prince has secured his seat at Dragonstone and ascertained the loyalty of the Maester there will Rhaegar and Prince use coded letters, so Ned inquired about the Prince's progress in training with the gift Ned gave, anyone who reads that will assume Ned was asking about the Prince's training with the swords Ned gifted, but only the Prince would know that Ned was asking about meditation.
Once the letters were promptly sent Ned dove back into his studies and personal training. He practiced fighting with enhanced senses Ned gained by pulling on his bond with Ironeyes, initially it seemed his skill at arms have degraded because Ned couldn't properly cope with having enhanced senses while in combat, but once he got better handle on it Ned experienced a sharp increase on in his combat ability, his kinetic and dynaic vision, situational awareness, sense of balance and reaction times increased sharply. He also learnt that the nearer Ironeyes is to Ned the less it taxed the direwolfs energy when Ned pulled on the bond. And that the more Ned practiced the skill, the less energy it cost. At that discovery Neds initial assumption that this skill would be useless when both Ned and Ironeyes are on same battlefield is revised. Ned sensed that there will come a point when decreasing cost of the skill will plateau, but Ned hadn't hit that point yet. Ned wanted to test the limits of this skill and took Ironeyes on a hunt in the nearby woods, from the beginning of the hunt Ned had the skill turned on, and even after spending half a day on the hunt, Ironeyes had more than enough energy to spare. It seemed the cost of the skill didn't start spiking until Ironeyes was more than four miles away from him and Ned has a feeling that four miles limit will increase as Neds magic and his control on it grows greater.
Ned tried another experiment, this one he started with household animals of horses, cats and dogs. He didn't want to make a bond with any of them, he only wanted to find out if he can form a one way bond which will let Ned read their thoughts and intentions. Initial experiments were a disaster. In the span of a week Ned accidentally warged into six housecats, all of which fought very hard against Ned when they noticed Neds presence and gave him blinding headaches, unsurprisingly cats have very strong egos and really didn't like it when Ned warged in to them. Ned double checked to make sure there are no lingering bonds with cats, the bond is really a two way street, a beast can hurt a Warg greatly if the Warg wasn't on guard as Ned learnt through experience. When he accidentally warged into horses they spooked, they reacted with panick. The stable hands were very confused about their fear. One such spooked horse almost caved in a stable hands head in its wildly panicked flailing, after that incident Ned thanked the Old Gods profusely and decided to never run any experiments on horses. That left dogs, Ironeyes cowed all the hunting hounds, guard dogs and even normal dogs who stick around for leftovers and to hunt rats and other vermin alongside cats in to submission in his first two months stay at Eeyrie, and these canines are usually submissive towards Ned too. When Ned accidentally warged a guard dog there was expected aggression at the beginning, but as soon as it identified Neds presence, it gave up all fight and became submissive, this held true for every dog that Ironeyes established dominance over. Ned learnt a lot from these experiments but not what he started them for in the first place. Theoretically what Ned is trying to do should be possible, Warging is a art of mind, it lets a Warg establish a bond with another mind, read the intentions and feelings of that mind and usurp the control of its body, even if the mind that was being read and usurped is an animal one, so ultimately a lesser mind, it is still a mind. That means Ned should be able to stop the Warging process at the reading of intentions and feelings stage. But Ned couldn't form these theorized partial one way bonds, he was missing something, but he will keep at it.
The first reply he recieved was from Bran and contained good news. He had selected three boys who grew up in Winter towns orphanage and are fiercely loyal to House Stark and devoted to Old Gods, he started their training in Warging and had them bond with three raven chicks, they will ready for deployment in half a year. They will be trained in information gathering by accompanying Bran as personal guards for a year before being seeded into towns and villages near the castles or castles itself of Northern Lords. Bran seemed excited about their progress.
Next he received two letters from Winterfell, first one Lya and Ben wrote together, they reported on their progress in training at arms, it seemed Lya has a talent for all martial pursuits, as Ned expected. Ben asked when Ned would come home for a visit, Ned didn't have an answer for him. The second letter from Winterfell was by his Lord Father, and what he has to say is not good. While everything his Father had to say about Lya and Ben, treasury and larders of Winterfell, progress on the Moat and construction of new grain storages is good, the good news ended there. When Father gave the leeway for Brandon to choose his own bride from any of the eligible Northern Ladies, it seems Bran has started vacillating, and that there is some talk of Bran taking up with whores and even bedding Barbrey Ryswell. It seems Bran has more in common with Robert than I initially thought. Father said that if Brandon will not decide in next three months, he will decide for him. And negotiations with Hoster Tully have stalled, apparently the man wanted both his daughters to wed Heirs of Great Houses, and spares are not good enough for him. Hoster wants his eldest daughter to wed Brandon and younger one to Jamie Lannister. Is there no end to Hoster's ambitions, Ned wondered.
They need the Northern Lords placated, the new found mines, the Ironwood venture and Wintersteel has seen to that House Stark grew wealthy, even if the South didn't think much of that wealth, the North certainly would, it is imperative that House Stark is seen to have best interests of the North and that they are willing to share their newfound prosperity with their fellow Northern Lords. Having two sons of House Stark betrothed to Northern Ladies will have to be enough, that left Lya and Ned. What he has in mind for Lya will have to wait atleast another two years. That left Ned, Hoster Tully didn't pan out, that means Riverlands are out, there are no needs for anymore ties with the Vale and Stormlands, Neds fosterage has seen to it, Westerlands Ned wouldn't touch with a ten foot pole. Reach will probably disdain them, but there is no harm in making enquiries, if a port town is established alongside the new castle, which is going to be Benjens seat, then transportation costs for grain could be reduced to a tenth. Ironborn are out of question, that left Dorne, there are possibilities there, Ned would have to read up more on it before making any plans.
Ned wrote to his father suggesting to give up on Hoster Tully for now, and betroth Benjen to Dacey Mormont and start pressuring Bran to make his decision. Ned also implored his Father to not make any matches for Lya, saying that he has someone else in mind for her and will explain more when he met Father in person in six months at Moat Cailin. Then he finished by once again reiterating that they need that Castle and port built on western coast as soon as possible, as it's existence can make importing grain from Reach less prohibitively expensive and considering a match from Reach not a pointless idea, he also suggested looking into expanding trade with Dorne, North and Dorne might be very far apart, but they are equally outsiders to rest of the Seven Kingdoms, that connection has potential to exploit.
The letter from Rhaegar has subtly implied that his skill level in meditation is progressing and that he will go to Dragonstone and secure it in a month. And that he has started working on his promise of aid, there is apparently a ship that has already set sail from Kingslanding containing fifty men who are sentenced to the Wall, another fifty men and boys who have no prospects at Flea bottom and volunteered to join the Wall encouraged by the gold incentives Rhaegar promised to either their families or themselves and fifty Targaryen household guards to keep them in line. And Lord Jon Connigton, a friend of Rhaegars, who is secretly carrying twenty thousand dragons Rhaegar promised as first installment of taxes that weren't paid by the South to the Wall in last few decades with twenty household guards of his own for protection. Alongside all of them a Journeyman Architect from the Architects Guild at Kingslanding, who hasn't been promoted due to Guild politics, is journeying with his whole family, apparently the Architect jumped at the opportunity to have years of study work with repairs and reconstruction of castles at the Wall and a chance to earn patronage of House Stark if his work gained approval from Starks. The Architect will settle his family in Wintertown and journey to the Wall to join other builders in their efforts at repairs. Rhaegar has spoke highly of his skills, apparently the man has worked on some projects for the Prince in last four years. The letter from the Prince raised Neds opinion of him a few notches. The man really works at keeping his word.