Good books on the Old Testament that are accessible to the general public are rare. One I can recommend is:
James K. Hoffmeier, The Archaeology of the Bible (Oxford: Lion, 2008).
Hoffmeier covers both Old and New Testament from an archaeological point of view. He has a light touch and is able to convey the subject matter without getting lost in jargon. Hoffmeier's specialty is the Old Testament and so his discussion of the Old Testament is stronger than that of the New Testament. Even those familiar with the material will likely learn something new.