That's it, really. I want to learn about this culture and time.
You could try Babylon by Paul Kriwaczek.
Do you want it just about Babylon, or is the whole of Ancient Mesopotamia ok? If it is I'd recommend Civilizations of Ancient Iraq by Benjamin Foster and Karen Foster. It does have about Babylon in that
There's Babylon by Joan Oates. It's not popular literature, but it's not impossible either.