Just a few comments since I live in the area (Mpls) and grew up in Appleton:
For Appleton, Chicago would probably be the closest and cheapest for a flight/bus. It would also depend on if you use a certain airline as Delta would go through Mpls. Of course if a parent is visiting they can always fly into Appleton for a little more money and convenience. Many colleges have buses to major metro areas over the holiday (Mpls to Lawrence and also Madison and Indiana to Chicago, I know of,…so something to check but I think it’s fairly common and safe).
Carlton is in Northfield, MN, 30 miles south of the airport. Grinnell is in Iowa and may be closer to Chicago? Neither are considered strong music schools. They may be considered good…so they could be a great fit for the right student to continue music study with a focus on academics. However they do not have the reputations of Lawrence nor St. Olaf for music. If you are looking at Carlton, you may want to stop by St. Olaf (right next door in Northfield). It is a selective, academic LAC but not in the same category as Carlton. For music however it is very selective. It does have the MN Lutheran-lite atmosphere. You certainly don’t need to be religious…but just in case that would be an issue.
So, if you do decide to come to the north part of the mid-west to look at music schools, Lawrence and St. Olaf would be worth considering IF a high-level of music is important. I do think Lawrence has maybe more of a serious academic, dual degree feel and St. Olaf tends to feel a little more like an exploration of liberal arts and music. But that’s just my opinion. Of course Carlton and Grinnell have great reputations for academics (just less so for music).