There is a range in Ellisville that has been mentioned above.
Lake Gep is a skeet club. Great group of guys but it is only open twice a week and only for skeet.
There is also Ellisville Dirt Pit Shooting Club which holds matches off of Gandy Cemetery Rd. off of Hwy 590. As far as I know, the "Dirt Pit" is only open for matches though. Encoreman on here will likely have more info, but feel free to PM me about any of the above if I can help, and welcome to the forum.