Since you have your permit, and Missouri honors permits from all states, the only places illegal for you to carry in this state are;
1. Any federal property,
2. Post office and property of,
3. Public transportation - airports beyond security and pretty much any buses and trains since you can't check your baggage,
4. Indian reservations. - Are there even any in this state?
5. Within 1000' of a school zone (you are only exempt from the Federal Gun Free School Zone Act if you posses a permit issued by the state that the school is in.
ALL other prohibited places, you can be charged with an "infraction" which carries a monetary fine, but no criminal firearm charges.
You CAN be charged CRIMINALLY for trespassing, if you carry, get caught, and are a jerk when asked to leave, in the prohibited places.
You are SUPPOSED to be asked to leave if caught carrying in a prohibited place, and if the police are called, that is when the infraction kicks in.
Let's face it. Most people in these places are not going to approach and ask you to leave if they know you have a gun, the police will probably be called right off, which means instant infraction/fine/possible trespassing charge.