Could someone please recommend a good book(s) on the Neo-Babylonian Empire (circa 626-539 BC) or King Nebuchadnezzar II? Of particular interest would be something talking about the cultural practices or everyday life of the period, but general history would be helpful as well. Some light google searching has not produced many results.
If you haven't already checked it you should look at the booklist that /r/AskHistorians keeps: https://www.reddit.com/r/AskHistorians/wiki/books/middleeast#wiki_ancient_near_east
It doesn't look like there are any specific books for what you are looking for but I would recommend A history of the ancient Near East by Marc Van de Mieroop, it covers the period and is a pretty good read.
For general overviews of Babylonia, see Trevor Bryce's Babylonia: A Very Short Introduction, Gwendolyn Leick's The Babylonian World, and Joan Oates' Babylon. The best overview of ancient Near Eastern civilization is Liverani's The Ancient Near East: History, Society and Economy, which includes a chapter on the Neo-Babylonian period.
The main book for the reign of Nebuchadnezzar is unfortunately in French (Arnaud's Nabuchodonosor II, roi de Babylone). You could try The Reign of Nabonidus, King of Babylon, 556-539 B.C. by Beaulieu, though it's getting a bit dated.