Babylon is a single archaeological site, but it is a vast one. Allow at least half a day, ideally with a guide who can point out what is genuinely ancient and what is Saddam-era reconstruction. The processional way, the foundations of the royal palace and the ziggurat depression all lie within easy walking distance of each other.
The original Ishtar Gate and most of the famous glazed brick reliefs are in Berlin's Pergamon Museum and the Iraq Museum in Baghdad. What you see here is a smaller-scale reconstruction at the original location, plus the genuine foundations beneath.