Are you absolutely sure that the facility is operated by The City, regardless of the property ownership? Is there any possibility that The City contracts to a private corporation for operation of the facility? This is a scenario not outside the realm of possibility. If it is contracted to a private corporation, they can probably ban guns. Not that it's right - just legal.
I only ask because I would hate for you to send an email without the proper background information, and then be seen by them as uninformed. I find in these situations research before action results in a better outcome.
I'll write the email for you but let's make sure everything is in order first.