When people think of rivalries, they most likely think of Ohio State-Michigan or Yankees-Red Sox, but when I think of rivalries, Johnnies-Tommies comes to my mind. If you don't know these two schools, here's some quick facts.
University of St. Thomas - Campuses in St. Paul, Minneapolis, Owatonna, and Rome, Italy, 10,839 students, very good at basketball (2011 national champions), baseball (2009 national champions, and my brother plays there), and softball (2004 and 2005 national champions)
Saint John's University- Campus in Collegeville, Minnesota, all-male, 1,917 students, has a sister school College of St. Benedict that is all-female, very good at football (1963, 1965, 1977, and 2003 national champions)
These two schools HATE each other, and they're both Private Catholic schools, which is odd. The Johnnies normally dominate the Tommies. The Tommies have got closer and closer to taking down the Johnnies until they finally ended a 16-game losing streak to St. John's in 2010.
St. John's football stadium is called Clemens Stadium, named after William Clemens (as you can tell, I'm a huge Johnnie fan). It was named on of Sports Illustrated's Top 10 Dream Destinations due to it's "natural bowl" like shape, and it's beauty.
If you want to see a huge rivalry, but on a smaller game, I recommend you make the trip up to Collegevile.