In fact the NCAA simply uses the mileage from campus to the arenas to pick the sites. Whichever arena is the closest to the overall number one seed's campus, that's where they go. Then whichever arena is closest to the overall number two seed's campus, that's where they go.
Unless they change their past practices they won't even say something like "well these two sites are kind of close for this school, if we move them to the further away site it will make it a lot better for the next team on the list so let's do that."
Here is a real world example of what I mean. If we were a protected seed and when they got to us on the list to assign our pod to a regional Columbus was full but there was a spot in Albany (460 miles away) and Greensboro (428 miles away) we would get assigned to Greensboro. They wouldn't say well if we put Pitt in Albany, which is a little worse for them, we can leave Greensboro for Virginia, which would clearly be better for Virginia. In that case we would go to Greensboro and Virginia would go to Albany (or somewhere else).