The outcome will vary from state to state, jurisdiction to jurisdiction. In my neck of the woods if you don't take your pistol/revolver with you and choose to leave it in the car, it will be added to the impound/inventory document and secured in the car. If you requested that the police take custody of it for safekeeping, we would do that, although there is no legal responsibility to do so. We would do it out of compassion/service for the requestor. We do not however take anyone's property without legal justification unless requested to. Even then the evidence technicians cry about having to secure "safe keeping" property. Believe it or not, some folks never come and secure their property and the evidence technicians end up having to add it to the huge inventory of accountable property that has to be inventoried yearly.
In GA, for a weapons permit holder it's not a crime to carry a pistol/revolver into a place with a "No Guns" policy. I personally would conceal it, carry it, and go about my business. As always, YMMV.