The hecklers tried to get him to react, but the mayor was unflappable.

Calm, unflappable, oblivious to danger.

Steady, determined, unflappable. A simple man who was good at simplifying problems.

There is a delicate difference. "Suave" means smooth; a suave person is a smooth talker. "Urbane" derives from the word for a city; an urbane person is sophisticated. Both words suggest someone who is unflappable; an urbane person may be even more unflappable than a suave one.

Grant didn't like the war. Although fearless and unflappable in peril, he deeply suffered for the misery and pain and the spectacle of bloodshed that the war was causing upset him profoundly.