jdege covered Minnesota's situation pretty well. It's worth noting that while local store managers tend to panic, large companies at the national level have already realized that CCW doesn't pose a threat.
In Minnesota, the Target empire (Target, Marshall Fields, Mervyn's) doesn't post. Neither does KMart, Wal-Mart, any major grocery store, nor most chain restaurants like Applebee's, Friday's or the Macaroni Grill.
Many hospitals and health clinics are posted.
Very few banks posted, and several of those have since changed their mind.
Some local bars and restaurants in St. Paul posted for a while, but a string of armed robberies helped convince them that disarming the place -- and then advertising it -- was not a good idea.
Let people wail in Missouri. Pass out the "no guns/no money" cards. Be polite when you explain to managers that the sign will only keep out paying, law-abiding customers, not bad guys. Send a short, polite, well-reasoned email to corporate HQ.
You'll soon see the rest of the state realize, in the words of our local wag, Joel Rosenberg, "The sky isn't falling." In time people will wonder what all the fuss is about.
And if you feel you need to go into a posted place, go in. The worst that can happen, in the unlikely event that you don't conceal well enough, is that they ask you to leave, and you cheerfully comply. No laws broken.
Matt