If you carry concealed and there are no metal detectors and no one pat you down at the door, I say you should ignore the sign, provided that you are not breaking the law. As long as you're not printing or otherwise not in any way advertising that you are carrying, keep your piece concealed if that's what makes you comfortable. Here in Indiana I don't see very many signs banning the carrying of weapons, but the few I have seen (ie., at Methodist Hospital in Gary) I just ignore.
To be honest with you, I know someone very close to me that basically does that exact same thing. Like most state laws, NC doesn't make it illegal
to carry a concealed weapon into an establishment with a sign, it simply states that the permit doesn't give you permission to do so. So, if it stays concealed, it's not a problem...and even it DOES become known, I'm breaking a private policy, not a law. No harm done unless I refuse to leave.
My point for openly carrying is to make a statement. If I show up with a gun hidden in my pants and try to talk to the manager about their policy, they're not going to take it too well if I make the "well I'm armed and you don't seem concerned about me" comment.
On the other hand, if I show up carrying openly, it allows them to make the first move. They can ask me to leave, and I can very politely and inquisitively talk to them about their policy, first making the point that their sign specifies concealed weapons, and then eventually trying to make the point that the more honest people with guns they let in, the safer they'll be.
They also may very well not say anything. They may honestly mean no concealed
weapons, and not have a problem with open ones.
I've done this at a few establishments around here. So far, they've all been chain stores, and their reasoning for the weapons ban was "the guys at headquarters told us to because of insurance liability." This place is difference, since it's a privately owned local diner. It's also a hand-made sign (8.5x11 white paper with marker on it).