The not black and white Mayor

[Wildfly]

"He's a politician" pretty much sums up Wilkins' personality perfectly. The typical image of the politician is to appear to be totally concerned with and dedicated to the welfare of his constituents while in actuality pursuing his won hidden, and usually self serving, agenda. At times, that agenda requires actually doing something that might be considered "good," but it is done in order to advance his own evil plans.

As for Wilkins' relationship with Faith, I've always thought that he was written in such a way as to be a dark parallel to Giles, just as Faith was written to be Buffy's dark counterpart. Each Slayer was given the father that they needed and actually didn't have. Buffy and Giles being the yin to Faith and Wilkins' yang.

Wilkins referrals to his long dead wife might simply be part of his politician persona, since the average voter is more likely to vote for a family man, even a widower, than a bachelor.

A charismatic politican with his agenda, absolutely agree, except the part about his wife.
Politicians also have feelings and he probably really cared for Faith and his wife (else he easily could have killed and replaced her instead of suffering long years with a senile woman)
PR is everything for people with careers that open their lives to the public, but that little speech he gave to Angel and Buffy felt genuine to me. What interest he had then to appear in a better light to people he intended to eat in a few days?

He was pissed off that Angel chose Buffy over Faith and so he lost an useful pawn, but still he was sincere. He shared his personal experience of a love between an immortal and mortal. Angel probably believed him and the mayor's input influenced his decision of leaving. (Well, that and the spinoff)