We'd need less than the current roofspace. Compared to existing enterprises like agriculture, the land use is pretty small. Is still huge, of course, like the same size as Spain, or just over half of Texas, but spread out globally that is technically reasonable to achieve.

edit - The problem with most nuclear technology, is that if you are looking for a solution to global energy, it has to be something that you are not going to be scared of your enemy possessing. Nuclear might be cheaper to implement in some scenarios, but it is geopolitically screwed as a ubiquitous energy source.