Do people in the US have that good a grasp of geography? I'm an Aussie like others on this thread and to expand on katycoo's example I used to live in (what I would describe as) the outskirts of Sydney. I won't name the actual suburb, but let's say North Rocks. About 45 minutes to CBD, up to an hour or more in traffic, but there's no actual gap - it's definitely part of the same greater urban mass.
If I met someone in Sydney I would say "I live in North Rocks"
If I met someone in the central coastal NSW I would say "I live just out of Sydney" or "I live on the edge of Sydney" and elaborate if asked.
If I met someone from pretty much anywhere else I just said "Sydney" - because why do they need to know where I live and why would they know where the heck North Rocks even was, anyway?
Now I live in the largest city of my region (not very large, mind you, but quite well known) and I can't imagine rolling my eyes at someone saying they were from my city when really they were from a small town half an hour away. I know they're not trying to be part of 'my tribe' or trying to look cool and urban, they're just giving an easy answer to a small talk question. It's small talk, for Pete's sake.
OT - I lived in a small country town for a while and when a city friend made a disparaging comment about people who don't live in cities I just said "Oh? Where do you get your food?"