At least one non-Mormon says that it is very nearby--just across the Missouri River in fact: Oklahoma Joe's BBQ In Kansas City [KS].
Me? I thought that the text of Genesis pinned down the location of the Garden of Eden to somewhere in the Middle East:
And the LORD God planted a garden eastward in Eden; and there he put the man whom he had formed. And out of the ground made the LORD God to grow every tree that is pleasant to the sight, and good for food; the tree of life also in the midst of the garden, and the tree of knowledge of good and evil. And a river went out of Eden to water the garden; and from thence it was parted, and became into four heads. The name of the first is Pison: that is it which compasseth the whole land of Havilah, where there is gold; And the gold of that land is good: there is bdellium and the onyx stone. And the name of the second river is Gihon: the same is it that compasseth the whole land of Ethiopia. And the name of the third river is Hiddekel: that is it which goeth toward the east of Assyria. And the fourth river is Euphrates…
We know what the Euphrates is. The "Hiddekel" river is the Tigris. It makes for a rather large Garden indeed that includes the Anatolian headwaters of both, but it is rather far from Missouri...