what kind of organism is a city

Cities are complex things and forgetting for a moment about the human social interactions there are so many things and places and interactions with the environment that make it perhaps better represented by a complex multicellular organism.

If you are unfamiliar with this line of thinking, consider Conway's game of Life. Which is a basic simple set of rules on a checker board. The rules are simple, based on any random (or chosen) starting of checkers on the board which squares will remain covered, which will "die". The graphic at left is an example of stepping though these rules and showing how this "thing" moves across the board in a simple motile behavior. Sure, its not living, perhaps its not real ... but then when you look at the biochemistry of just one part of your body (say insulin production) that doesn't look alive either.

Given that Cities can't easily move a static organism is perhaps best which is why I often choose a plant for my comparisons. The interesting thing is though that most plants get their energy needs from the sun while cities rarely get their energy from the sun (although this is changing). So perhaps cities can be compared with the Monotrope family of plants.

These plants are quite unusual in that they rely on relationships with Fungi to survive (and so they're called Myco Heterotrophs). I think this quote from Wikipedia sums up the city well enough too.

Myco-heterotrophs can therefore be seen as ultimately being epiparasites, since they take energy from fungi that in turn get their energy from vascular plants.^{[3] [4]}

This isn't far from a city, as the energy for a city is mostly from the burning of fossil fuels (most electricity is generated from burning fossil fuels) but some solar and some animal power still serves.