So let's just assume his excuse is false and he was actually there having sex with the journalist. Let's be honest, he almost certainly was. If you lose respect for the guy over the act or the lying to excuse it and don't want to vote for him to represent you, I get that. If you're his wife and want a divorce, absolutely. If you're his child or family and embarrassed by his behavior and don't want to be around him, fine.
Short of that, like... who gives a shit? "He's got to pay" "It's an insult to the city." Really? Because he had casual sex with another consenting adult that isn't his subordinate? Because he did that in a (closed) government building? Why does that matter? Why does that need to be punished? Why does he need to lose his career over it? Of all of the less than righteous things someone in a leadership position could do with their power, the thing I care the absolute least about is consenting adult sex in a government building after hours. Hell I'm not even an adventurous person and I've had sex parked in a dark parking lot and in a closed store. Should I "have to pay" for those dalliances, and lose my career over it?