Renting a car would be easiest. If you prefer not to, Harrahs has an airport shuttle that runs at the top of each hour (the airport is only 15 minutes away). At the airport, you can catch the Metrolink which provides good transportation downtown with many other available stops as well.
I'm not sure if you can get to the brewery from the Metrolink, but it does have stops for the Arch, Busch Stadium, and several shopping malls. Their website is www.metrostlouis.org. I've used this many times when I didn't feel like driving downtown for Cardinal games and it's very easy.
IF you do rent a car, driving and parking in downtown STL is quite easy. You won't believe how wonderful the arch is, pictures don't even begin to do it justice.
diane