Yes, I know he lives on Drury Lane, but where is Drury Lane located? I thought it was in Far Far Away, but the Shrek Wiki says Duloc, since Lord Farquaad knew about him. I changed Duloc to Far Far Away on the Muffin Man's Shrek Wiki page, but it got changed back to Duloc? So which kingdom does he live in?
The Gingerbread Man apparently lives Duloc during the original Shrek, being close enough for Lord Farquaad to torture in the first movie. He mentions the Muffin Man, but we do not see the Muffin Man in that movie, or have any indication of where he lives (aside from "Drury Lane"). Watching only Shrek, we might reasonably conclude the Muffin Man lives in Duloc - why else would Gingerbread Man and Lord Farquaad discuss Drury Lane so casually?
However, in Shrek 2, we see the Gingerbread Man reunited with the Muffin Man, and they conspire to create Mongo and storm the castle in Far Far Away. Given the distance between Duloc and Far Far Away ("pok!") it seems clear that the Muffin Man lives in Far Far Away.
I would say that, having watched only Shrek, it would be reasonable to assume that the Muffin Man, and Drury Lane, were in Duloc. But to move Shrek 2 along, the Muffin Man was concretely placed in Far Far Away.
So the answer is different depending on which movie you want to reference.