Tarrence’s answer above is a great example of how archeology tends to validate more than invalidate the basic historical reliability of the Bible. Also, check K. A. Kitchen’s book On the Reliability of the Old Testament for about the most thorough exploration of the issue (as it relates to the Old Testament) designed for popular audiences. Concerning the New Testament, F. F. Bruce’s classic The New Testament Documents: Are They Reliable? is also very accessibly written and well worth the short time it takes to read through it. As Tarrence mentions, anything by Lee Strobel will be helpful and well researched. Josh McDowell is another contemporary American author who approaches this subject similarly to Strobel. Finally, I cannot recommend enough that you familiarize yourself with the work of N. T. Wright. He has written extensively on the subject of Jesus’ resurrection and its historical veracity. A very accessible essay of his can be found at http://ntwrightpage.com/2016/07/12/jesus-resurrection-and-christian-origins/.
Above all, it is important to realize that even if it can be demonstrated that something in the Bible is not 100% historically accurate, that does not discredit the Bible, either in its basic historical reliability or in its theological value. First, there is no such thing as history written without slant. All history (and that includes modern historiography) is written with some kind of slant. But that slant does not mean that what is written is of no value. Actually, one might argue that it is precisely the slant that gives the historiography meaning (otherwise unrelated events are tied together into a coherent narrative). In any case, it means that you have to read everything with an awareness that the author has a purpose in writing it.
Moreover, a robust Christian theology of the Bible must take into consideration the idea that God has chosen to partner with humanity in his self-revelation and mission of salvation. In other words, we don’t diminish the fact that the Bible is written by humans, in human language, and using human tropes and conventions when we say that it is also God’s special revelation. God uses the humanity of his human partners to accomplish his divine purposes. That’s what redemption is really all about – God taking what seems to be counter to his purpose and turning it around for good as if he always meant it to work out that way – and it’s why God is so awesome.