Origin of the expression "his/her face is a map of the world"

Solution 1:

It means their face is old, wrinkly or weathered, or that the marks on their face can be related to the contours and marks of a map. It can be negative (saying they're ugly) or complimentary (saying they're experienced). It's not a particularly common phrase, but the sentiment isn't unusual.

Published in Bentley's Miscellany in 1840 is this from Greenwich and Greenwich Men by J. Hamilton Reynolds:

To what reflections do not the passing of these stunted, distorted, crinkley-faced battered, shattered, homely wrecks of valour and patriotism in cartridge - not Bath-nove - lead! One man leans, with a face like a map of the world he has sailed round, beneath a huge granite gateway - and he is not all before you! No; - one eye parted company at the Nile, at the night hour when the Orient exploded in the eyes of the shore-bordering Egyptians,- a leg had previously been tossed to a shark that hungered in the troubled and bloody waves which rolled from the Baltic around the "leviathans of the deep," close to the walls of Copenhagen!

This Fool's Cap Map of the World is from around 1590: