It could be South Dakota, Nebraska, Kansas, or Missouri. It depends on your definition and range of southwest, but Nebraska probably is the best answer.
Lincoln, NE is around 430 miles SW of St. Paul MN - so depending on your definition of SW this is the closest to the 400 mile mark.
St Paul, Miinnesota.
Maldives
400 miles
a couple in Phionex and a couple in Glendale
Joaquin developed as a tropical depression approximately 400 miles southwest of Bermuda.
That would be Montana, however the distance in road miles is longer than 400 miles to the southern border of the state.
It is 400 miles according to Google Maps.
Utah.
400 sq miles
Utah
If you drove 400 miles west of Denver you would be in Utah.