A personal note, the word "unbiased" instantly raises red flags for any academic who'll call up in his/her brain the entire history of social theory and the problems of presuming there can be such a thing.
But we of course, understand what you're getting at. An alternate phrasing for future reference might be "accessible and academically well-regarded."
It means roughly the same as what you're getting at, but the word "unbiased" tends to bring the knives out.
Rather than giving you foreign policy/political-science books; the two books I highly recommend for interested people, to getting a proper understanding of today's Middle East, would be these two books:
"The Arabs: A History" Eugene Rogan
A History of the Modern Middle East William L Cleveland, Martin Bunton
If you want to understand the situation today, its important to take a historical approach to it, rather than a political-science one, written by pundits and politicians, who carry a lot of the interests of their respective backers.
They are standard University texts, very well written, and updated as well. To understand the "present", one must first understand the "past". And so if you want a truly unbiased understanding of the Middle East in 2015, its important to understand how events got to there.
Hi There! The responses can be a bit off-putting so far because such a seemingly simple question sparks a huge nerd fight over who is any one given contributor's favorite/least favorite author. In stead of giving you a list of books, instead let me give you some insight up front, regardless of whose book(s) you read.
First, there is no such thing as "unbiased" - it is a nice idea, but most historians, politicians, and journalists have certain sympathies. The key question is "are they honest about their biases." By that, I mean is the author telling the reader that they are coming at the subject from a certain perspective (usually in the foreward) such as mentioning why they felt the need to write this book, where they studied, and so on. With that said...
Second, don't let the debate raging here (and it would get hotter if it was allowed to) dissuade you from reading some of the books mentioned by the contributors, such as /u/Slarotimov and /u/The_Turk2. Don't worry about whether historians take so-and-so seriously when choosing a book recommended here; that's an academic debate that has its roots in the fact I mentioned above. It is better, by far, to read a controversial book than it is to rely upon news stories. "As for what is not true, you will always find abundance in the newspapers" - Thomas Jefferson
Finally, be specific in your desires to read; when you say "the conflict in the Middle East" I immediately wonder "which one" - the civil war/Saudi intervention in Yemen? The war against Daesh in Iraq and Syria/The Syrian civil war? The Israeli/Arab or Israeli/Palestinian conflict? and so on. If you want to know about any one of these topics, there are numerous books upon them, but I would recommend, in general, that you stick to University presses. By-and-large university press books are more thoroughly researched and scrutinized than commercial presses. Additionally, I'd wave you off of pundits (i.e. Bill O'Reilly, Glenn Beck, etc.) as they mask their agendas with plausible-sounding disinformation or a distorted analysis. Interestingly enough, a good place to start is right here on /r/AskHistorians as there are a LOT of threads and FAQs on the many conflicts in the Middle East, from sectarian to political to resource-based and everything in between. Best of all, you get a feel for what the hot topics and brightest thinking is in the field today without having to wade through books that can, at times, be really dry. Search through this thread and you'll see what I mean.
Good luck and we hope to see you again here soon.
There is no unbiased source. Every source leans one way or another. The question is how far they lean, and whether they are aware/provide other perspectives too. That is crucial.
For history on the Israeli-Palestinian conflict, Righteous Victims by Benny Morris is good. He leans pro-Israel. For contrast, Charles D. Smith's Palestine & the Arab-Israeli Conflict goes the other way. Both are well-respected in the field and stray away from the major extremes on either side, like Efraim Karsh on the pro-Israel side and Rashid Khalidi on either side.
As a note, be aware of two things:
Biased sources hold a lot of value. They shouldn't be perused at first/alone, but they tell a significant amount about perceptions on either side of a conflict. That's extraordinarily important. History is not just a list of events that occur and move on, in books. It does tell a story that is important for today's implications, which is what most want to learn about. Also, more biased sources can include what might seem trivial to outsiders, like an event others don't think (as observers) is important, but which informs a key part of a group's psyche and historical narrative. As an example, a history book that tries to be neutral might stray away from documenting both narratives of what happened or did not happen in a particular massacre during war (preferring to simply pick whatever it feels is most credible), while a biased source and its counterpart would tell you more about the event's importance through how it tells that story.
Broad sources are good. It's nice to get a broad overview of things. But be wary, and don't think you're an expert for it. Broad books tend to seem unbiased, but actually have some biases because they're so constrained for space. It's hard to include both sides of a complex issue if you have little space because you're covering so much. Broad books are a place to start, not a place to feel you are hugely informed from. They can help you know more than most, but if you bump in a discussion against someone who's done more than broad reading, they'll be able to quickly inform you of events you had never even known existed in history. So be wary of overestimating your knowledge based on them. I don't mean to discourage you from exploring them, but far too often I see someone who read a book by Morris, Khalidi, or someone else who thinks they know it all. It just isn't that simple.
I have studied the Middle East for a long time and I don't think you will find an unquestioned source. Almost all historians, researchers, and journalists are questioned by some party who think they are not analyzed well. If you find yourself an objective reader just start with the basics, the history and culture of the Middle East, although it may not be unquestioned you can do research for yourself. Events and facts that are mentioned are easily re-searchable nowadays.
Personally I am a big fan of several Israeli and Jewish authors regarding the Middle East (and more precise the history of Israel).
Easy accessible sources with Good information are:
It is also interesting to read sources with a strong opinion. You don't have to agree with them but it gives you a basic understanding of how certain people think. I think a famous example of someone I don't totally agree with is Edward W. Said. He makes strong points about the Occident and The Orient, social constructions, arguments I can really use in general but I don't agree with him overall. I don't think it makes The West necessarily the bad one and The Orient the victim. Regardless it is an interesting read.
Examples:
If you are interested in a Book about how the Middle East is portrayed, the influence of Media, then there is also a specific Book that I would like to suggest:
Ofc there are many more Books and Works but I think you can start with the snowball method from here (use the sources the Publications above use for example), online material as Al-Monitor are also Good to start your research from and come in touch with experts and authors, much to find.
Don't try to find the objective masterpiece explaining everything that is going on in the Middle East, form your own opinion based on several sources, you can do the fact checks to large extents yourself (or make comparisons between authors).