Other recommendations are always welcome, but in the meantime you might be interested in our book list on the area.

Additionally, I might recommend The Ancient Orient by Wolfram von Soden. The author is a philologist, so the skew is definitely towards cuneiform as the primary evidence, but they do incorporate a good bit of archaeological evidence. It is also definitely a survey of the field which means you aren't going to get a tremendous depth in any one subject, but it does cover just about everything to a greater or lesser degree.

The big downside being that it is about 25 years out of date at this point. This isn't totally damning for archaeology/philology like it is in other fields, but it is something to consider. The Van de Mieroop book on the booklist is probably a better choice in that regard, at least to start with, but reading both wouldn't be a waste.