The name Sinai, according to Rabbinic tradition, derives from sin-ah which means hatred. This is a reference to the other nations being jealous of the Jews because they received the Word of God.
The actual location of Mount Sinai has long been debated. The prophet Elijah travelled to the mountain when he flees from Jezabel . After this occurrance there is no other reference that suggests that anyone knew the location of the mountain.
The Sinai Peninsula
There is evidence that prior to AD 100 early Jewish pilgrimages had already identified Jebel Musa as Mount Sinai and that Christian pilgrims later adopted the location. Josephus wrote that "Moses went up to a mountain that lay between Egypt and Arabia, which was called Sinai." Therefore this location has traditionally been called the true Mount Sinai. Interestingly this location is actually a collection of peaks that appear to be one mountain as one would enter the grouping.
As Moses was tending the flock of his father-in-law, Jethro, the priest of Midian he came across the burning bush on Sinai. Since evidence suggests that the Midianites resided near the Gulf of Aqaba it would also suggest that Sinai would be near their territory in Saudi Arabia.