You are correct, I do not live within city limits but please let me know...who the hell would? I would also hazard a guess that of the 38-40K that show up on gameday, the majority come from the suburbs where I live.
When I refer to "our" city, I would guess that most denizens of the suburbs would describe it the same way and when they go away anywhere and are asked where they live...they ALL say Syracuse. I was born there and only live about 5 miles outside. So yes, I believe "our" is appropriate.
As far as "our" interests, by being the mayor of the city she has a responsibility to the city first, understood, but she also has to look at the big picture for the region and work together to make things better for all of CNY. It's called being a leader, which she clearly is not. Caretaker maybe of place filler, yes, until a real leader gets elected with some vision.