I've been going out to an @slu game for about seven years straight. And I just want to point out a personal do and don't for explorer fans traveling to St Louis.
DO visit the bars and restaurants on broadway. Not the new Cardinal town that was just built in the last few years. I mean the historic important ones, like BB's Jazz Blues and Soups ($5 cover on Wednesdays) and Broadway Oyster Bar.
Rather than the hassle of renting a car/cab at the airport, you could ride the RED line metro which runs door to door between airport and downtown hotels, including an intermediate stop at "Grand" which is 3/4 mi from the Chaifetz Arena. It runs til midnight and starts up again at about 4:15 AM. This convenient, reliable and modern system allows you to transport quickly to and from the airport every 12 minutes or so. Costs $2.50 per ride, plus a $1.50 "tax" for leaving the airport. Day passes are $7.50.
DON'T show up at the game an hour late. Time zone difference! The game is listed at 8 PM Eastern but it really starts out there at 7:00. I can't believe my first trip to SLU back in 2005 when they joined our conference, I actually got to our game that was half over. It should have been quite clear, but I was having so much fun in the city that I hardly noticed the time!