Below are some resources I enjoy and find useful in understanding biblical archeology and getting updates on new developments and excavations. Also check out My Archeology Blog Articles for information on artifacts that have been discovered that are significant for understanding the land, scriptures, or people of Israel.
The Armstrong Institute of Biblical Archaeology (AIBA) puts out some of my favorite resources and currently has one of the most important excavations happening at the Ophel, and the City of David. They have a great podcast that makes learning very accessible. As well articles that are easy to access online. They have a free bi-monthly magazine that has great material and delivered to your door that I really like.
Israel Antiquities Authority (IAA), although a government agency of Israel, has many good resources and the largest library of archeology publications. They are the custodians of the dead sea scrolls and research associated with them. They also have very important excavations happening currently at the pool of Siloam, the western wall, and the tower of David. I find their information to be important by a lot harder to access and sift through.