It sounds like another case of a local government elected official not knowing the law and thinking he IS the law in his town.
To summarize, the city can't regulate open carry ANYWHERE. The areas where open carry is not allowed are created by state and federal laws. Concealed carry may be regulated in government buildings (roof and walls) but only after that policy is passed as a local ordinance. The proper signs must be conspicuously posted at the entrances, and the buildings can't be residences. There can be no criminal penalty assessed for violation of the no CCDW local ordinance. Employees of the city have a different situation. Their employer (the city) can establish employee rules prohibiting guns at the workplace (locked in the car in the parking lot should be OK).
There are several ways to proceed. Some have recommended being cagey and not showing your hand too soon. There is value in that strategy sometimes. I generally prefer the other approach. I keep some strategic information in reserve, but I usually prefer to share as much public information as soon as possible, in a friendly, helpful and non-threatening manner. If they're going to be jerks about it, it'll become contentious soon enough, but I don't want to be the one to start in that direction. I'll err on the side of assuming they're well meaning but misinformed, and I'll try to correct their ignorance by showing them the law.
Here's a good Kentucky League of Cities checklist to help the city determine what's legal and what isn't:
http://www.klc.org/sectionArticles....ces & Solutions and Solutions/Legal/Legal New
I also record almost all of these conversations, in person or over the phone. I want a record of what was said... by both parties. It can be very handy later.
It's a pity that we can't fix this problem and be done with it. We seem to be condemned to constantly fight these battles over and over. It costs us time and money, and our tax dollars PAY our elected bureaucrats to repeatedly deprive us of our rights. It not only costs them nothing, it actually pays!
Good luck!