If I was High King of Skyrim...
I would relocate the capital to High Hrothgar for starters and teach my people the ways of the voice.
Then races of all kinds would be welcomed to Skyrim, as long as they didn't bring war with them.
My third act would no doubt be to capture and re-educate falmer populations living within underground reaches.
Also- seizing of dwemer technology, giving magical understanding to the populace and permitting necromancer to an extent-
That is which so that the practioners do not disturb honoured dead, but rather try their magics on creature corpses or permitted excises.
Other than those, I'd no doubt try to crush any remaining imperial prescence within the province and try to persuade any unracist stormcloaks to my side.
After dealing with the province itself, I'd move to make political ties with orsinium and hammerfell. Hoping to squash High Rock from both sides.
Then to move onto making deals with dunmer / argonians, if successful - invade cyrodiil while hammerfell recovers from any serious losses.
If the Empire gains aid from the Thalmor to drive back my threat, then I'd look to Paarthurnax- hoping that he might sway a small league of dragons to my cause.
Who knows? a united dragon empire under a Dragonborn would be intriguing to see once more. But that is what I'd do at any rate, if I was the High King.