Where did the Sioux live before the europeans came?

Almost nobody lived on the High Plains of North American until horses were introduced by the Spanish. The very few tribes that hunted buffalo on the Plains lived on the margins and used dogs for transportation, but without horses it was extremely difficult to follow herds across the vast distances involved.

In 1700 (some 200 years after Columbus arrived in the Bahamas) all the Sioux tribes were living around the Lake Traverse area of what is now South Dakota - not in the central Plains but on its eastern margins. They were under considerable pressure from the Ojibwe/Chippewa groups who were armed with guns supplied by French fur traders and were being forced to move westwards. At that time the Sioux had no guns and no way of obtaining them, so in military terms they were losing the arms race.

By 1780 they had moved further west towards the Black Hills, the more westerly tribes (the Teton Sioux) having obtained horses and adopted a Plains nomadic lifestyle.

So the answer is that some Sioux tribes (not all) lived in the central Plains from about 1760 or 1780 and were forced onto reservations about 100 years later.

It was the white people who created the Plains culture by providing access to horses; it was also white people who ended Plains culture by eliminating the buffalo herds, imposing the reservation system and destroying the nomadic lifestyle.