We've stayed at the Casino Queen, directly across the river from the Arch, more times than I can count. While you DEFINITELY don't want to be wandering around East St. Louis, if you come into St. Louis, you can cross the Mississippi on the Eads Bridge (the one just to the north of the Arch). At the end of the bridge, make two quick lefts and you're there. Clean, excellent security, a little bit of train noise. As someone else mentioned, security will give you a lift to the MetroLink station at the casino, and it will drop you off right across the street from the third base entrance to the stadium.
If you have a toad and don't mind staying out a little distance consider Red Barn Rendezvous at Exit 23 on I-55 near Edwardsville, IL. On the Missouri side, the City of St. Peters has a very good park at exit 2 on Highway 370, just north and west of St. Charles. Babler State Park and the Eureka KOA are also good options that others have mentioned.
As for the St. Louis RV Park on North Jefferson, you couldn't pay me to stay there.
