The ancient city of Babylon is located at about 100 km of Baghdad. At the time I was there, the only possible way to get there was to rent a taxi for half a day (about 10$) and it is about a one-hour ride. The archaeological site itself is very interesting not because it displays rare artefacts but because most of it was rebuilt by Saddam Hussein 12 years ago. The site is actually new, with a fake gate of Ishtar (The real one is in the Pergamon Museum in Berlin), and fake palaces built 1990. The only "real" thing is the lion statue that is a bit outside the palace of Nabuchodonosor.
When the site was discovered, most of the interesting artefacts where taken by the German archaeologists and very little was left behind. Saddam decided to rebuild the place after the Iran-Iraq war as the proof that the Iraqi People was a great people. No more hanged gardens or ancient ruins similar to the ones in Egypt or Greece, but instead a "Disneyland" type of archaeological site.