Start at the centre of the city. Collect a core sample every 10 metres (or whatever unit you agree on) - be it a piece of sidewalk, a poster, a piece of garbage, whatever, as a way of getting a picture of that city.

This is based on some Techniques of Participatory Rural Appraisal that uses a strict, mathematical formula to try to get a quick idea of the make-up of a new rural region for development work. I learned it from a book I read while in the Peace Corps. It sounded neat and fun and structured but kinda useless. Basically, in involves picking a starting point, and then a distance - lets say 10 metres - and then taking samples every ten metres - of soil, garbage, piece of a wall, whatever is at that point. It is supposed to be an objective way of analyzing a rural area so that we know what we are doing when we "develop" it.
But when we apply it in our own place it starts to seem kind of silly - even psychogeographical - much like the Ghana Think Tank took development strategies and rendered/ exposed them as ridiculous when reversed/ applied in our own contexts.
One way to approach it is to simply display the results, perhaps with a report analyzing what we know of the city based on that evidence alone. Another way is to arrange a swap. We each do it in different cities (or ask other people to do it in other cities) and mail each other the samples, which are then placed in the related spots in the sibling city.
More on PRA techniques
http://www.scn.org/cmp/modules/par-tech.htm
The image is more a concept thing than an actual method, though that would be cool as hell to be able to do, trading actual square metres of city!!!!!