I recently noticed that the mental map I'm building of NYC is not that different than my mental map for Philadelphia. (Before we go further, I convess to a gepgraphical prejudice of thinking of Manhattan as being the most New York of New York, with the other bits (from Yonkers to Queens and yes I know Yonkers is not legally part of NYC but I think of it as being part of it) being distinct bits of New York that are more their own thing).
Both of them are, in a North-South orientation, dangling above a river with bits of city outside. and a smaller river heading up the left after the main dangle. Philadelphia's downtown part maps to Manhattan, Camden to Queens, and a lot of relatively uninteresting bits of New Jersey map to Brooklyn. (Obviously not a cultural match). University City, unfortunately, maps to Newark and Jersey City, while the weird-shaped bit of land PHL's airport is on maps to Staten Island.
That last mapping is pretty weak; Staten Island is huge, far bigger than Manhattan, although I only know this by looking at Google Maps; the functionality-oriented transit maps seen in NYC always show it as being relatively tiny (presumably because it's less populated and has fewer stops). I like the idea of importance-weighted maps, either using population as a substitution metric or seeing them drawn by people. Before I left ColumbusOH, I made one of those for the city, and it was interesting seeing others say they would draw certain regions larger or smaller based on where they visited.
Just to show that the geographical stuff is silly, I can imagine trying to map Pittsburgh onto this, if I'm allowed to rotate the map a bit. Downtown Pittsburgh near the peak being Manhattan, Mount Washington being Brooklyn, the North Shore being Newark (sorry!), and .. actually, if we're going to ignore where the heart of the city is, it might be fun not to rotate and imagine the North Shore as being Manhattan, Pittsburgh proper as being Brooklyn/Queens, and Mount Washington to McKees Rocks as being Jersey. Ha! Take that!
Until I was heading down to pick up a mislaid U-Haul truck, I had never really left Pittsburgh to see the scarydepressinghickish areas around it. It was pretty eye-opening. I'm glad that the PortAuthority stretches reasonably far out there.