I'd go to Riften and visit Haelga's Bunkhouse.

I'd live in Whiterun so I could get to the cloud district very often.

live on the road, travel everywhere...

meet everyone and learn to be a true scary badguy hero leading all the guilds... who would suspect the archmage to be leader of the thieves and dark brotherhood...

If we assume that I would even survive in Skyrim:

Paarthurnax would obviously be first on my list. Come on, he's a DRAGON, how cool isn't that?

Then I would want to see what I would think about Marcurio and Ulfric IRL. I would probably hate them both, lol.

As for places, I would like to see the major cities: Whiterun (including a visit to Dragonsreach's private balcony), Windhelm, Markarth, Solitude.

Then I would go to Raven Rock. And from there, Morrowind.

During the time I'm playing it is real to me. I would do exactly what I did.

Maybe ill stay at the temple of High Hrothgar and enjoy the freezing weather with the greybeards. LOL!

I would head straight to Valthume, running all the way with no breaks, ram an enchanted dagger right into Valdar's stupid face before he can even utter a word, and sell my soul to Hevnoraak immediately.