Map via the Wikipedia entry on Mesopotamia
One problem. Contrary to the account of 1st century CE Jewish historian Josephus (in his defense, probably due to inaccuracies in the sources he relied upon), they weren't built by Nebuchadnezzar and they weren't in Babylon in what is modern day Iraq a little bit to the South of Bagdad.
Old research showing an absence of any archaeological evidence or historical writings in places where they should exist strongly disfavor this location. Instead, new research including ancient written sources (although not yet archaeological evidence) now strongly supports the conclusion that the Hanging Gardens did exist, but that they were located instead in Nineveh, which in ancient times was near the modern city of Mosul, and were built by Assyrian King Sennacherib, a century before the reign of King Nebuchadnezzar in Babylon.
Notably, the new location is also geographically closer to all of the other seven wonders of the ancient world, while Babylon had been a geographic outlier of the seven.