Any info would be great, but I'm thinking in terms of things like culture, politics, and religion.
#Religion:
The religion in Ancient Israel and Judah could be called a forerunner to Judaism. The majority of the people were monotheistic, and followed God, whom they called Yahweh. The main language of Judah and Israel was ancient Hebrew.
Most early semites were polytheistic. For example the neighboring Kingdom of Moab was polytheistic, with the chief god known as Chemosh. The Book of Numbers states that the Moabites induced the Israelites to partake in their sacrifices. King Solomon even built a "high place" for Chemosh on the hill before Jerusalem. These nations all partook in similar religious activities, and, over time, their religions seemed to unify together.
#Politics:
Most of the neigbors of Israel and Judah had similar political systems, being monarchies. Some of these include the Kingdom of Moab, the Kingdom of Edom, the Kingdom of Ammon, and the Kingdom of Arab Damascus.
After Israel divided into two Kingdoms, Edom became a dependency of Judah. The King of Edom was most likely and Israelite that was appointed by Judah.
The Philistines are one of the major antagonists in the Bible, and seemed to be the greatest enemy of the Israelites. They seemed to be in a perpetual state of war with the Israelites, and the famous Bible story of David (Israelite) and Goliath (Philistine) shows the violence between them. In the Bible, God directed Moses in his exodus so that he would specifically divert the Philistines.
The Politics of the Philistines were different. Philistia was a Pentapolis comprising Ashkelon, Ashdod, Ekron, Gath, and Gaza. These cities were in a federation.
#Culture:
This is similar to religion, as in that time, religion and culture went hand in hand. Almost every country had their own form of religion. At that point, the cultures of Israel, Judah, and their neighbors were much more similar than they were after the next few centuries. The Edomites were eventually converted to Judaism when it became a more solidified religion. Before then, they most likely partook in the activities of the Canaanite religion.
Much of the information that supplies the facts that we know about the time period comes from the Bible.
Sources:
Fahlbusch, Erwin; Bromiley, Geoffrey William (2005). The Encyclopedia of Christianity, Volume 4:
http://www.jewishvirtuallibrary.org/jsource/History/Kingdoms1.html
Ahituv, Shmuel. Echoes from the Past: Hebrew and Cognate Inscriptions from the Biblical Period. Jerusalem, Israel: Carta, 2008
Jeremiah Chapter 48
Tubbs, Jonathan (2006)"The Canaanites"