A billion bucks is probably short of what's needed but I think a good lawyer could find out just how much it will take in a few questions during discovery.
“The punishment should ALWAYS be proportionate to the wealth of the slanderer ~ else there’s no element of punishment.”
Moreover:
1. False accusation of a crime is “slander per se.” Thus, damages are presumed.
2. The mayor’s false accusation has made it impossible for her to get a fair trial in NYC, so she should move to transfer her case.