What native American group moved place from place?

The Sioux tribe had to move from place to place about every 3 months when the buffalo migrated. The buffalo's gave them food, clothing and shelter and would have died without them. They moved their tipi's quickly to follow the buffalo.

Further to the above answer - In fact, it wasn't JUST the Sioux that 'moved from place to place'- all the buffalo hunting Plains nations were nomadic or semi nomadic, they had to be to follow the herd. That said, most of them did settle in a winter camp for the cold months.