I've tried a few missions now but I'm a bit confused still with how large a zone really is. Is there any indication somewhere where one zone ends and the next one starts? (outside of buildings)
On the streets a zone is a variable-sized area edged by building walls and pedestrian crossings.
From the Zombicide rulebook (page 5):
Inside a building, a Zone is a room.
On the street, a Zone is the area between two pedestrian crossings and the walls of buildings along the street. A single Zone may extend over two tiles or even four tiles.
For example, in the following image, the red boxes identify the different zones of the map: