As a Chicagoan, as much as I'd love another game in Chicago, the neutral site idea isn't a winner for me. Rivalry games need to be played on campus. It would be like playing Duke/Carolina at the Bobcats stadium. Likewise, the United Center is a massive arena. It's the 2nd-largest arena in the NBA by capacity (Only the Palace of Auburn Hills has more). Compare to a full Bradley Center against the Irish. (
http://www.youtube.com/watch?v=z4rfKAO9tMM)
Think about how hard it is to fill the Bradley Center. Now add another 2,000 empty seats, and move the game almost 100 miles from campus. MU has nothing to gain in this arrangement.
In an ideal world, MU can set up a mid-term (4-year) or long term (10-year) contract with ND for a home-and-home. Hell, let's even start it on the road next year. MU would play Notre Dame at home in December of even-numbered years (the years that MU plays at Madison), and play in South Bend in December of odd-numbered years (When Bucky comes to Milwaukee). That way, MU would be guaranteed to have one big non-conference rivalry game every year at home, and also one non-conference road game pressure cooker early in the campaign to judge progress.
Selfishly, and this will probably earn a ragging, but I'd love to see Marquette restart their series with Northwestern. I've wanted to see a game at Welsh-Ryan, and MU could probably take over that arena pretty easily. Likewise, getting NU at the Bradley Center would have to provide a bigger test than any of the alphabet soup schools that comprise the buy game schedule. The only potential setback is NU would probably only agree to a home-and-home, rather than a 2-for-1 or something like that which would complicate nonconference schedule for other marquee opponents (i.e. Ohio State).