Mankato is a real town located in Minnesota, not far from Walnut Grove, which is why it was used as one of the settings for the the Little House on the Prairie TV Show. Mankato is about 90 miles from Walnut Grove, so in the Ingalls time, it wasn’t a place they could visit in a day (by today’s standards, it takes about 90 minutes to drive between the two towns at highway speeds).
There is no evidence the real Ingalls family ever lived or spent significant time in the real Mankato. The town of Mankato does not appear in the Little House books, nor in the original Pioneer Girl manuscript.
The TV show was not filmed in the real Mankato, Minnesota.