How should anthropologists approach the city as an object of study?
Anthropologists should approach the study of the city by using a mixture of traditional anthropological approaches along with methods that would more commonly be associated with sociology.
Traditionally, anthropologists have tended to study smaller, more "primitive" societies. These could be relatively well observed through participant observation. Cities are too big and complex to be thoroughly studied in such a way. Therefore, it will be necessary to make use of such things as census data and surveys.
However, this is not to say that anthropologists should simply become sociologists when studying cities. Instead, they should still do things that are more common to anthropology such as looking closely at the experience of a small group of people within the city. They can then use the experience of the small group to try to enrich the lessons that they learn from the more macro-level data they get through more sociological methods.