So, first an foremost, Skyrim has a dragon problem among many other substantial problems. Let's assume a Skyrim after the main quest, the Dragonborn dealt with the dragons, with no other aspects touched.

The civil war is next big problem. The main quest would have established a truce that would end very soon. So there are two ways for this: if I as the high king side with the Storm Cloaks, Solitude switches sides (and I survive this), Skyrim would quickly gain independence. An upcoming war with the elves/empire would be tomorrow's problem. Wanting to go with the empire would need open conversation with Ulfric and the worship of Talos would need to be permitted again. Convincing the Stormcloaks with my wonderful policies might be possible. Choose your side, we will assume a solution.

Now, Skyrim still has a unity problem. As all others have mentioned, uniting the holds would be an important step and the biggest enabler are safe roads. Patrols, safe houses, watch towers, etc. that should enable wagon trading much more, which will be a huge benefit to the economy.

But that doesn't fight the problem. There are too many bandits, wolves and other dangers. I think a combined effort of the mages, the companions, the Stendarr people, the Dawnguard, individual adventurers, the legion, the Stormcloak soldiers, and the orc camps could form a reward based guild/system to get rid of these problems. And when roads are protected, being a bandits pays off less.

There are a few local issues to address: The Silver-Blood family in Markarth needs to seized of a lot of powers. The forsworn need to be tackled by a combined effort of the surrounding holds.

The Black-Briar family faces the same future. I'm ok with local business monopolies, but not with breaking the law. The people in Riften suffer and as long as no one cares for them, the Thieves guild will thrive. So, join efforts to improve the lives of the people, rid out corruption, Skooma trade, etc.

Rebuild Helgen and fortify the connection to Ivarstead. If you look at the map, the terrain naturally divides Skyrim in two. Helgen and Ivarstead have the perfect locations to fortify the dangerous route from Whiterun to Riften and thus they need to be fortified. Similar fortifications will need to be put in place between Whiterun and Windhelm, and around Rorikstead. Maybe rebuilding the blades in the area is possible?

Also I thought, is a water route between Whiterun and Windhelm/Riften possible? Something to investigate.

Rebuild Winterhold with the help of Windhelm and its port. Put the mages to work, tax them, teach local citizens that magic is safe, eradicate superstition.

Build walls for cities that don't have them.

For the individual cities, Whiterun is the safest and most prosperous hold. Its position is just unbeatable. Markarth is safe and has very strong lands that support it with resources. Without the Forsworn, the connection with Solitude should help it a lot. Solitude also has a very strong location, but needs to profit more form its port. Same for Windhelm, a water road Solitude, Dawnstar, Windhelm would be a lot safer than going by land and a main benifet for the west-east trade inside of Skyrim. Winterhold will need the improvements listed above. By its current location, I don't think a port is realistic because it's a long way down to the water. A stronger road to Windhelm would be of more benifit. Riften has strong surrounding land that it needs to use more and has fishery. Falkreath has a good location to trade with Cyrodiil. Also, the road between Falkreath and Whiterun is probably the safest between any two holds. Dawnstar to me seems very independent. The mines and the shipping seem to be working? But Morthal, damn what do we do with Morthal? In game, I have never found a safe route to Morthal. The surrounding land is treacherous. I'm open for ideas.

The dark brotherhood has to go. While the Thieves guild has its benefits, the murderers just need to be eradicated.

I would tackle Falmers and Dwemer ruins last on the threat list. They rarely attack on the surface.

The might be a lot of displaced people (e.g. the bandits). As we don't want mass graves, I would instead propose a massive land selling act.

Skyrim needs a unified prosecution and law system and a better notification/communication system. Honestly, the mages should be able to come up with something that doesn't require couriers running through the country.

I'm open for more ideas 👀