Well, the two J schools that are most generally ranked "best" by the trade publications, professional societies, etc. are Missouri and The Scripps School of Journalism at Ohio University. Northwestern has had a strong reputation for years in print journalism.
So, in theory, they probably should have the best newspapers.
In reality, I think it depends on the group of student journalists who happen to be working on any given publication in any given year.
You can look at "The Post," the newspaper at Ohio University online at:
http://thepost.baker.ohiou.edu. Click on the "Today's Edition" button to see the entire paper.
I'm familiar with it because it's my Alma Mater and I started reading it when our daughter was in school there several years ago.