I can't honestly say that I know anybody who lives in the suburbs that won't reply with the name of the nearest major city when asked where they're from by a total stranger. Why would I want to be any more precise than I have to be? I don't know these people from Adam. Heck, look at the lengths posters have gone to in order to obscure the actual location of their residence on this thread alone? "MajorCity" or "MajorCity Area" is perfectly sufficient to answer a stranger.
Now that I'm back in my hometown, I actually have a double layer of this. Most of the time, I'll answer the question with Miami (since I've admitted several times where I live, I have no problem naming the general area here). Now, the actual city of Miami is quite small compared to the area that's known as Miami. There's Miami Beach, Miami Lakes, Coral Gables and many other smaller incorporated areas, along with a ton of unincorporated areas known as "unincorporated Miami-Dade County." Other than Miami Beach, most outsiders really don't know or care about those details. Now, I live in an area that got a huge amount of national attention due a major hurricane a while back. I could say the name of that city, but even then that wouldn't quite be the truth. Locally, I'll just say "SmallCity", even though I actually live in an outlying area of said small city.
I guess you can say that I live in a suburb of a suburb.