General background: Van de Meiroop, A history of the Ancient Near East

Babylon: Joan Oates, Babylon

Van de Meiroop also has a biography of Hammurabi, I believe, and an interesting book on daily life in old babylonian Ur. What are you looking for and what time period? Things changed considerably over time. More specifics to go on would be helpful.

Marc Van der Mieroop's A History of The Ancient Near East is the standard overview of the political history of Mesopotamia and The Oxford Handbook of Cuneiform Culture is really your best one-stop-shop for Mesopotamian culture and society. If you're working on a novel, do you have a good sense of the time and place it's set in? Mesopotamia is a large area and a lot changed over its history so it may be easier to provide useful references if you have a more precise date an time(for instance Nippur in 1900 BCE is very different from Babylon in 800 BCE is very different from Uruk in 2400 BCE).