I’ve encountered plenty of claims for something to be the “world’s oldest map” (most of which depend on how broad or narrow your definition of “map” is). One I wasn’t aware of until recently is this Mesopotamian map on a cuneiform tablet, which dates from between 700 and 500 BC, currently held by the British Museum. “The map is sometimes taken as a serious example of ancient geography, but although the places are shown in their approximately correct positions, the real purpose of the map is to explain the Babylonian view of the mythological world.” More at Visual Complexity. Via Cartophile.
For other claims to the world’s oldest map, see the following Map Room entries: Engraved Rock Is 14,000-Year-Old Map: Researchers; Candidates for the World’s Oldest Map; The Other World’s Oldest Map; The Western World’s Oldest Map.
Update, Feb. 20: John Padula points to this reconstruction.