I have some property on the border of Iron and Reynolds Counties on the Black River near Annapolis and find quite a few yotes. Also some feral hogs in the area (open season on hogs in MO). That area would be right at about 2 hours from St. Louis depending on what part of town you're in. I live in Kirkwood.
I have seen more coyotes this year on camera than any other year. I hunt I Maries and Miller county and after deer season I am going to start hunt em down. From my house down 44 I can be at out place in about 2-2.5 hrs. There lots of cattle farms down that way and I am sure if you stop and ask farmers would grant permission to hunt coyotes.