If you notice, several rivalries (like KU-Mizzou and OU-Texas) are currently played at neutral sites. There should be more neutral site rivalries IMO.
Here are examples of which rivalries should become neutral site:
Ole Miss-Miss State (The Egg Bowl) - Move to new 75K-80K seat stadium in Jackson, MS (an older stadium hosted the game from 1973-90).
Florida-Florida State, Florida-Miami (once that resumes) and Florida State-Miami - move those games to the Citrus Bowl in Orlando once renovations are complete.
Alabama-Auburn (Iron Bowl) - move to Birmingham, at a whole new stadium near the site of the current Legion Field. This game used to be played in Birmingham a lot, but believe me it needs to be moved back. UAB can even help fund the new stadium's construction (they would also be the primary tenants).
All football games between the NC schools in the ACC - Move them all to Bank of America Stadium in Charlotte, NC. In addition, Duke and NC State as well as UNC and Wake Forest can play a non-conference game each year in years which they are not scheduled to play each other in the conference.
Cincinnati-Ohio State - This rivalry is currently not staged every year, but if it does, it can be played in Cleveland (at the Browns Stadium) and have a trophy for the winner - perhaps a Governor's Cup?
SMU-TCU - Move this game to the new Cowboys Stadium in Arlington once it is finished
Indiana-Purdue, Notre Dame-Purdue, and Indiana-Notre Dame (this should be played every year too) - have all those games played at Lucas Oil Stadium in Indianapolis every year.
If you agree with these and/or have other ideas for neutral site rivalries, post!