Indeed. The bigger threat isn't a Mad Max world of anarchy outside of the opening days; it's what kind of social structures will grow out of a soil as tainted as that which will result from the destruction of so much of humanity. In times of calamity, extremism and rule of strength tend to gain far greater focus. Drastic measures taken in order to be seen as "doing something," religious or philosophical concepts twisted in order to perceive some sort of order and reason (especially the latter; altogether too many people like believing that there is some act, even malevolent, behind any disaster, some consciousness that can be placated or blamed) behind the apocalypse. Insularity may become the norm, and with it, xenophobia.
That said, don't count out the danger of cities to their hinterland in the near term. Billions of people live in individual cities (according to the UN ever since 2007, over 50% of the world's total population, in fact), and if a disaster strikes, there will be a mass exodus that will overwhelm the cities' hinterlands as well. Modern agriculture is utterly dependent on industrial infrastructure - synthetic nitrates for fertilizers, mechanization for labor multiplication, complex water systems for irrigation whether it's from aquifers or rivers (especially in places like the Great American Desert, AKA the western Midwest, AKA half of the American breadbasket and the Canadian Palliser's Triangle), and perhaps worst of all, tailored GM crops that don't produce viable seeds to permit next year's harvest. The collapse of social order in the wake of any apocalyptic event will greatly disrupt this infrastructure. Even in some rural location commonly perceived as "podunk" or "flyover country" such as, say, Kansas, cities could turn into a potential time bomb: the population of Kansas is 2.8 million; compared to this, the adjacent Kansas City metropolitan area shared with Missouri is 2.4 million, and not all of that will flee into Missouri just because they're on the east side of the border. Farming isn't just a matter of picking up a hoe and tilling the soil; even if you put the entire population to work farming, it would be...painful, to say the least, and people are unlikely to lie down and simply die, to watch their own loved ones die, just because they happened to live in the wrong place.