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 a wide range of peaks and valleys in the narrative of the Israelites. Some of the peaks include the miraculous deliverance of the Israelites from slavery in Egypt, the revelation of the Ten Commandments at Mount Sinai, and the construction of the Tabernacle. On the other hand, some of the valleys include the grumbling and disobedience of the Israelites in the wilderness, the incident of the golden calf, and the prolonged journey through the desert due to their lack of faith.
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.