Depends on your stats. With high enough stats, Alabama is a lock, and Utah has good aid with the proviso that the student has to become a Utah state resident (which is more easily possible there than in most states). We’ve also found that Ohio has scholarships designed to bring high-stats OOS students in. Those are all I have off the top of my head, but there are a handful more.
As far as base tuition, in addition to your mention of Minnesota, the flagships of Alaska, South Dakota, and Wyoming have quite inexpensive OOS tuition, Massachusetts, Arkansas, and Idaho a bit less so but still quite reasonable. There are probably others that should be on this list, but I’m in a bit of a rush.