It is Legal to Carry a Firearm into a Public Building in Utah..., so as long as The Public Building does NOT Qualify as a 'Secure Facility'.
Local Governments are Preempted from Regulating Firearms in Utah, so Salt Lake County or Salt Lake City CANNOT Regulate in This Subject-matter.
However, in Order to either: 1. Load The Firearm, OR 2. Conceal The Firearm; You must have a Permit Issued by Utah or a State in which Utah Reconizes.