According to Blue Letter Bible's A Chronological Map from the Creation to the Fourth Century A.D., it shows the Tower of Babel somewhere around the 23rd century BC. Answers in Genesis gives a date of 2242 BC.
Wikipedia's articles on Sumerian, Akkadian, Egyptian. Also, Ancient Near East - Periodization
Years | Sumerian | Akkadian | Egyptian | Other languages | Events |
Before 26th century BC | Archaic Sumerian | - | Archaic Egyptian | - | Creation |
26th–23rd century BC | Old or Classical Sumerian | Old Akkadian (2500–1950 BC) | Old Egyptian (2600 – 2000 BC) | - | Flood |
23rd–21st century BC | Neo-Sumerian | Old Akkadian (2500–1950 BC) | Old Egyptian (2600 – 2000 BC) | - | Dispersion of the Nations |
20th–14th century BC | Late Sumerian | Old Babylonian/Assyrian (1950–1530 BC) | Middle Egyptian (2000 – 1350 BC) | Minoan (Linear A and B), Phoenician, Mycenaean Greek, Hittite | Patriarchs, Exodus |
14th-10th century BC | - | Middle Babylonian/Assyrian (1530–1000 BC) | Late Egyptian (1350 – 700 BC) | Biblical Hebrew, Aramaic, Old Chinese | Judges |
10th-7th century BC | - | Neo-Babylonian/Assyrian (1000–600 BC) | Late Egyptian (1350 – 700 BC) | Classical Greek, Old Latin | Israel's United and Divided Kingdoms |
7th century BC to AD | - | Late Babylonian (600 BC – 100 AD) | Demotic (700 BC - AD 400) | Old Persian, Koine Greek, Classical Latin | Exile and Return of Israel |
2 Peter 3 verses 5-6 - "For this they willfully forget: that by the word of God the heavens were of old, and the earth standing out of water and in the water, by which the world that then existed perished, being flooded with water."