Mount Sinai is the place where God gave Moses the Law (Torah). This was in the region of Horeb and once called "Mount Horeb." According to Easton's Bible Dictionary, the word "Sinai" identifies the region associated by the ancient moon god, Sin, that Abraham would have known from living in Ur and then Haran.
It is impossible to pinpoint the exact location of this mountain, though tradition has it in the southern Sinai peninsular. The problem is, the peninsular was named based on the text of the Bible. It has not been easy, therefore, to verify any location exactly, though the clues in the Bible help the reader greatly.
The first mention comes early in the record of Moses' adventure as leader of his people. Having fled from the wrath of his adopted family — the royal family of Egypt — Moses had spent forty years working in Midian where he had begun a family. It was there, near the "Mountain of God, which is Horeb," he saw a bush burning without being consumed. The word "Horeb" simply means "desert, or wasteland." But Moses called this "the backside of the desert" and he had his flocks with him .
This indicates a plain with vegetation and near where the Midianites had settled. Midian was a son of Abraham and Keturah, and was sent to the east of Canaan . By all accounts they were south of Moab. This location, then would be near the southern border of Canaan. Moses tells his readers that this was eleven days' journey from Kadesh-barnea via "the way of Mount Seir" . The estimated distance of a day's journey is about 25 miles, making Horeb as much as 275 miles from Kadesh-barnea. However, with a wandering people numbering at least two million, the standard day's journey may have been quite shorter. Given the maximum, a place in southern Midian in what is now eastern Saudi Arabia fits well. This is a place now called Jabel al-Lawz.
The traditional mountain region, with four peaks of interest (one called "Jabel Musa" [mountain of Moses]), in the southern Sinai peninsula is about the same distance from Kadesh-barnea (also known as Kadesh [the Holy Place]). The separation from Midian is the only problem with this choice. The distance given between the giving of the law and the sending out of the spies seems to limit the location of Mount Sinai to one of these two locations. The location of the crossing of "the Red Sea" would determine which place is the best.