In the Bible the Holy Mountain is in Midian which would be Northeast present day Arabia. In the history of the travels of the Israelites out of Egypt no actual location is given for Mt Sinai. The assumption is made partially because of the name given the Holy Mountain is the same as the Peninsula. Washington, the city, has the same name as Washington the State but they do not share the same geography.
An aside. They wanted to call the state Columbia after the river. “No - that will be too confusing with the District of Columbia!” True story.