I recently provided some suggestions in Books on assyria, but that is just the tip of the iceberg, and there are many more specialized books on Assyrian religion, architecture, warfare and imperialism, medicine, etc. I'm happy to provide additional suggestions for specific topics.

Daily life depends a great deal on the time period – Assyrian society of the Old Assyrian period looks quite different from that of the Neo-Assyrian empire – as well as social class and location/setting (e.g. a city in the imperial core like Nimrud as opposed to a small town in a province). For an overview of urban life in Mesopotamia, see The Ancient Mesopotamian City by Marc Van de Mieroop, which draws heavily but not exclusively on texts from the Neo-Assyrian period.