The Negev is spelled Negeb in the Bible, and the King James Version translates it as "the south."
Although no specific geographical boundaries define the Negev in the Bible, the region extends between Beersheba and Kadesh Barnea from north to south, and from near the Mediterranean Sea to the Arabah Valley from west to east, an expanse of about 70 miles wide. In Bible times, the territory resembled an hourglass or figure eight turned on its side. On all but the west side, highlands and mountains border the Negev, but to the west it stretches to within a few miles of the Mediterranean coast.
Today, the Negev is the largest region in the modern state of Israel and includes more territory than it did in ancient times. According to the Encyclopedia Britannica, the total area of the Negev Desert covers about 4,700 square miles, “occupying almost half of Palestine west of the Jordan River and about 60 percent of Israeli territory under the 1949—67 boundaries.” Rather than a figure eight, current Negev is shaped like an inverted triangle.
(https://www.gotquestions.org/Negev-in-the-Bible.html)
Biblical Account
Abram
After receiving the Abrahamic Covenant and learning about the Promised Land of Canaan, Abram traveled toward the Negeb at one point during his journey in Canaan until severe famine drove him to Egypt. Pharaoh sent Abram out of Egypt, so he went into the Negeb then Bethel, (Genesis 12-13:7)
Abraham
From the spot he mediated on behalf of the righteous in Sodom and Gomorrah, Abraham journeyed toward the territory of the Negeb and lived between Kadesh and Shur; and he sojourned in Gerar where Abimelech took and returned Sarah.
Isaac meets his wife, Rebekah, after returning from Beer-lahai-roi
Abraham insisted upon a wife for Isaac being found among his father's house and in the land of his kindred, not among the Canaanites. She must come to live in the land promised to his offspring. He had his servant swear to this mission, and he found Rebekah for Isaac in the city of Nahor in Mesopotamia.
Isaac had returned from Beer-lahai-roi and was dwelling in the Negeb. Isaac went out to meditate in the field toward evening when he saw camels were coming. Abraham's servant told Isaac all the things he had done. Then Isaac brought her into the tent of Sarah his mother and took Rebekah, and she became his wife, and he loved her. So Isaac was comforted after his mother's death.
(Genesis 24)
Samuel
After fleeing from Saul to Philistia with Achish the son of Maoch, king of Gath, David made Ziklag his base of operations for military exploits against the Geshurites, Girzites, and Amalekites as far as Shur, to the land of Egypt. He reported his raids back to Achish as against the Negeb of Judah, Jerahmeelites, and Kenites and gained Achish's trust. (1 Samuel 27)
A band of Amalekites made a raid against the Negeb and against Ziklag. They had overcome Ziklag and burned it with fire and taken captive all the people, including Ahinoam of Jezreel and Abigail. An Egyptian servant of the Amalekites was left to die and revealed to David the band had raided against the Negeb of the Cherethites and against that which belongs to Judah and against the Negeb of Caleb, and they burned Ziklag with fire. (1 Samuel 30)