Growing up in Connecticut, "the city" was always New York. Of course, if you go somewhere else, though, "the city" changes. With that in mind I've always wanted to build something that found the footprint of different cities around the country. How far into New Jersey can you go until they start calling Philly "the city"? If you're in the middle of the nowhere is the city the next town over with 2,000 people?
I still don't know the answer and still very much want to build the tool/map out, but in the meantime
CommonCensus is the closest thing I've seen to an answer. It draws a map based on responses to "On the level of North America as a whole, what major city do you feel has the most cultural and economic influence on your area overall?" I don't think it's perfect, but it's still pretty interesting. Notice, for instance, the influence of Salt Lake City or Denver (both surrounded by not so much) as opposed to New York or Philly (where cities are more clumped together). Good stuff.