I just moved from there a while back. South west of St. louis there is a small shooting range called Monroe County Gun Club. They have targets to 500 meters and I had a steel target on a tree at 750 yards. This small range is near the town of Parris I believe. There is a member on here " Tyler Kemp" that lives close and I enjoyed shooting with him.
Paris has already been mentioned, but there's also St.Louis Bench Rest Club near Warrenton/Wright City, and further West we have Bucksnort shooting club near Marshall. Both SLBRC and Bucksnort go out to 600 yards, the longest we've got in MO.