I'm with you on the Boston and Chicago incidents, but I think that to lump Mayor Lee in with them, one has to read too much into what he says. Whatever meaning he intended--and I agree that he might've intended to be threatening official Mayoral action to block Chick-fil-A from locating in San Francisco, and even that if he was intending to threaten the use of Mayoral power, he likely intentionally chose his words carefully so as not to be held accountable for the threat he was making--he did not make a threat clear enough to warrant lumping him in with the other two officials in the other two cities. There are other possible meanings, and you're choosing the most damning one, and attacking him for what you think he meant, probably.
Mostly this is a disagreement of opinion--you read one thing into his tweet, and I read another, and neither of us has any definitive proof--or will ever have any, unless the Mayor says something more to clarify the meaning of that original tweet (and even then, he could be walking back his original statement, right?)--but you're also suggesting that what he said--what you believe he said--is a violation of law.
I don't think so. I don't believe there is any law under which one can be prosecuted for what folks think a person meant in a statement as unclear as his. (And even if there were some way to prove he actually meant he would take official government action, I question whether there would need to be some overt act--or some showing that Chick-fil-A suffered some quantifiable damage, at least--before a case could be brought against Mayor Lee.) But I'm not a lawyer, so what do I know...
And while we're on the subject of law, I'm still perplexed by your cite of Virginia v Black, and your suggestion that one can find "the law of what counts as a threat" as a part of that decision. As you may've read, all I found when I perused the thing was the cite about "true threats," which involve clear expressions of the intent to commit unlawful violent acts. And if you're reading THAT into what Mayor Lee said, well, I'd be very surprised.
I'm a little worried about the accusation of Mayor Lee in terms of free speech, as well. If your interpretation of his meaning is wrong, you're defining down what an attack on free speech actually is--and chilling the speech of those who would disagree with Dan Cathy, or with those who would defend him (I'm sure you recognize how being casually accused of a crime can put a crimp in one's speech)--and I think that's very dangerous.
Finally, I'm certainly not going to agree that the verbal overreach of a couple of elected officials--which they already backed off from, in the face of a whole lotta pressure from, well, almost everyone--constitutes an attack on free speech that would cause me to advocate for eating at a Chick-fil-A restaurant in the name of striking a blow for the first amendment.
I'm pretty sure that Chick-fil-A will see a good size bump in their business for a little while (and on Wednesday, for sure). The thing is, buycotts tend to be short-term. People do their duty and make a point of making those purchases for a little while, then life sets in, and the McDonalds is a half a block closer, and... people in the buycott start purchasing like usual, again.
The customers Chick-fil-A gains over this issue will almost certainly give the company a bump, short term. The customers they lose will likely never come back.
That said, I sincerely hope you enjoy your chicken, sir. I hear it's dee-lish. (The whole boycott/buycott thing is academic for me... The nearest Chick-fil-A location for me to eat at or protest is like 50 miles away... ...and at this stage, I'm not willing to make a day of it, however strong my beliefs...)