The Desert of Paran in Arabia or Wilderness of Paran (Hebrew מדבר פארן Midbar Par'an; Douay-Rheims: Pharan), is quite likely the place where the Israelites spent part of their 40 years of wandering. King David spent some time in the wilderness of Paran after Samuel died (I Samuel, 25:1). It is also the place where Abraham's wife Hagar and his first son Ishmael were taken (Genesis 21) and it features in the opening lines of the Book of Deuteronomy.
"Then God opened her [Hagar] eyes and she saw a well of water. So she went and filled the skin with water and gave the boy a drink. God was with the boy as he grew up. He lived in the desert and became an archer. While he was living in the Desert of Paran, his mother got a wife for him from Egypt. At that time Abimelech and Phicol the commander of his forces said to Abraham, "God is with you in everything you do. (Genesis 21:19-22, NIV)"
"He said: 'The LORD came from Sinai and dawned over them from Seir; he shone forth from Mount Paran. He came with myriads of holy ones from the south, from his mountain slopes.' (Deuteronomy 33:2, NIV)"
"These are the words Moses spoke to all Israel in the desert east of the Jordan--that is, in the Arabah--opposite Suph, between Paran and Tophel, Laban, Hazeroth and Dizahab. (Deuteronomy 1:1, NIV)"
"Then the Israelites set out from the Desert of Sinai and traveled from place to place until the cloud came to rest in the Desert of Paran. (Numbers 10:12, NIV)"