Moses fled to the land of the Midianites, once he realized that it was known that he killed a Egyptian. As it was a serious crime to kill a Egyptian master.
Moses fled into the wilderness for the first time after he slew a Egyptian.
To escape from slavery.
Moses
3-months after leaving Egypt, Moses and the Israelis came to Mount Sinai. Moses received the "Ten Commandants" and the plans for the earthly tabernacle. They were in the wilderness.
Moses leads the Israelites out of Egypt and through the wilderness to Mount Sinai, where God reveals himself and offers them a Covenant: they are to keep his torah(i.e. law, instruction)
In Egypt, and later in the wilderness of Sinai.
The Ten Commandments were given to Moses by God atop Mt. Sinai on the Sinai Peninsula, which is east of northern Egypt. Chapter 19 of Exodus describes the Israelites' coming into the wilderness of Sinai, and Chapter 20 describes God's proclamation of the Ten Commandments to Moses.
The Sinai Peninsula.
Moses, in keeping with God's guidance (Exodus 13:17-14:1).
Upon exiting Egypt the Israelites traveled to Mt. Sinai, which the bible informs is in nothern Arabia, most likely in the eastern part of the land of Median, the country of Moses' father in law. From there they travel to the area around the Jordan River. Here they failed in faith and for forty years they wandered in the wilderness until God brought the remnant back to the promised land.
The book of Exodus covers the peak of the Israelites' liberation from slavery in Egypt, the journey through the wilderness, and the establishment of God's covenant with them at Mount Sinai. It also includes the valley of the Israelites' disobedience, grumbling, and lack of faith during their time in the wilderness.
The giving of the law of God on Mount Sinai. God's miraculous provision of food and water in the wilderness - manna and quail and water from the rock. Quite a number of occasions where the Israelites grumbled.
It was the forty-year period (Numbers ch.14) that the Israelites spent in the wilderness before entering Canaan.
Egypt in the Ancient Period controlled far less land than Egypt in the modern period. Although the Sinai is now part of Egypt, it was not at that point and God did lead the Israelites through the Sinai, but did not direct them in Nile Basin (Ancient Egypt), which the Israelites would have been familiar with and thus would have needed no direction. It is important to note that while maps of Ancient Egypt show it "controlling" the Sinai Peninsula at various points, this "control" was through indirect vassals and tributes, not through a standing infrastructural connection.