Excellent but very detailed maps of ancient Mesopotamia can be found in:
Tübinger Atlas des Vorderen Orients (Wiesbaden: Reichert, 1977-1993).
The Beihefte. Tübinger Altes des Vorderen Orients offer additional geographical and historical information.
As part of the Beihefte, a series of studies of place names was published in the sub-series:
Repertoire Geographique des textes cuneiformes (1977 – present)
An ancient Mesopotamian map of the world, as drawn on a cuneiform tablet, can be seen in the British Museum.