From Baghdad, Babylon is about 1.5 to 2 hours by road, with typical round-trip taxi costs around 90,000 to 130,000 IQD. From Hillah, the drive is 15 to 20 minutes and costs about 15,000 to 25,000 IQD.
A budget option is a minibus to Hillah and then a taxi to the gate, but a private driver is more convenient. For more info: Babylon (Ancient Site)