Will the main villain of Skyrim (weather it be Alduin or someone else) have a major fortress or stronghold that he uses as a base, and that the player has to charge into to defeat him?

I thought that having to journey into Red Mountain and fight Dagoth Ur on his own turf was cool, but in Oblivion, the Mehrunes Dagon's home wasn't even in the same universe per se, and he came to you in the end.

Yeah that was cool in Morrowind. I doubt we will see it though, we are fighting yet another creature that doesn't call tamriel home.

But could he establish a base once he gets into into mundus or whatever? Esbern said "they're already here", they may have had time to set something up.

Alduin is an actual god, I don't think he has much use for a base.