"Babylon" is not a particular place It is "the world," that is the "nation" of those who "worship" the things of the flesh.
"Babylon is fallen" simply signifies the overthrow of worldly, fleshly power in favor of the Kingdom of God.
In saying this, of course, you disagree with Mr. Lindsey who claimed during the Gulf War that Babylon (as in Iraq) was a "real place." Hal has since "revised" that view I suspect.