Pappy's is the big one down town that a lot of people go to. Get there before 12pm to guarantee a full menu. They sell out of stuff before 2pm sometimes.
A good STL chain BBQ is Bandana's BBQ. Not the greatest but still worth the trip.
18.5" OTS, 22.5" OTG, CB Silver(Rip), Vintage Coleman Bullet, Pit Barrel, UDS