I have the data for several cities in a layer. I'd like to run a batch export, that goes through a list and zooms in on one city (coordinate + zoomlevel), then the next, etc and exports each results based into a pdf. Is this possible?
You can use the Atlas functionality of the Print Composer. You center-coordinate could be a point layer, with a point for the center of the city map or a bound of a polygon if you city is a polygon. The layer defining bound of map is called the coverage layer. The zoom level is either a margin on geometry or scale. You cannot data bind to the zoom level (yet), if you have zoom level as an attribute of your coverage layer (city layer). So you zoom level is either based on a margin around a polygon, a fixed scale or a best fit scale.
Setting zoom level of multiple Atlas prints.
What you want is the Atlas Generator in the Print Composer. This is exactly what it was created for.
There are a couple of tutorials which will help you achieve this: