Schlafly's Tap Room for sure.
Also I know it's "overrated" and commercial, but touring the Anheuser Busch brewery is pretty cool (and the Clydesdale Horses are awesome).
Q: What does Busch stand for in Busch beer?
A: Brewed Under Six Clydesdale Horses
If you don't mind a little bit of a drive (guessing you'll be staying down town), I recommend heading out to Main St in St. Charles, (i-70 west across the river to 5th st, follow the signs from there) there is a small brewery there called TrailHead, they have pretty good beer but really good food, however right next door to them is a little restaurant / pub called The Old Millstream. This place is a Diamond in the rough and definitely my favorite bar, they have got a beer selection that is truly fantastic, outside seating in a nature environment, a small but elegant food menu, you can pretty much catch my wife and I up there at least once every 2 weeks
If you go to Millstream, I definitely recommend ordering their cheese and sausage plate and team it up with a Schlafly Special Release American IPA.