I actually went to Rovaniemi two years ago, and visited Santa's home there, which sparked this initial question.
After hearing more about it today from a friend, that other places claim he has a different home, I figured I'd ask the question, and start researching too. It appears there's certainly several:
North America - both Canada and the US have traditions stating that Santa lives at the North Pole, and post goes to post code H0 H0 H0 (oddly, this is actually Montreal in Quebec). However there's no possibility of actually visiting a Santa at the North Pole, unless you bring your own. :(
Alaska - there's a town called "North Pole" there, which has a Santa Claus house, where Santa can be visited.
The Nordic regions - Each Nordic country claims they have Santa there - Norway claims he lives in Drøbak. In Denmark, they claim he lives in Greenland (near Uummannaq), in Sweden it's Mora, and in Finland either Korvatunturi or the place I visited - Rovaniemi.