Very interesting to see the different cities and I love the SLC maps with housing pics and prices to match.
As for the favored quarter theory I think it certainly holds some water. In Columbus it's the north and northwest (very DC-like).
Columbus' bad urban neighborhoods vary in a number of different ways, but by and large have little worth making the trek out and as a result Columbusites think anything not due north or northwest is one big gangland. Drug related gang shootings do occur on the greater east side (including northeast and southeast areas) where the most homicides occur and where you can buy a
house for cheap, but I know of two people who bought starter homes in the worst neighborhood in the city on the northeast side, South Linden, and one had his place broken into three times last summer and the other, well, she owned firearms and once had to lose a group of guys following her around from a rundown carryout to avoid them knowing where she lived. So as you can see it's bad in different ways. Where improvements have begun is mostly just east of Downtown where the housing stock is the best with a couple of small clusters of new retail.
The south and west sides are bad due to the dregs of small town Ohio and Appalachia forming a rather large portion of the population; we didn't exactly end up with people that they'd be missing any time soon. You know who I'm talking about, loud trashy neighbors with junk in their yard who punch their dogs (invariably pitbulls) for barking. Over on these sides of town there are less empty storefronts and not as many shootings, but you also get a contingent of meth heads and prostitutes on the west side along with businesses that won't attracts visitors like a whole slew of bars that local Yelpers are too scared to even set foot in, although I did get the ball rolling with one. The (due) south side has seen improvements whereas the west side has not. The northern 1/3 was gentrified thanks to the highly desirable all-brick German Village, while revitalization of the middle 1/3 has taken root in Merion Village (which is due more to proximity to GV rather than it's own aesthetics), and the last 1/3 is Steelton which has more than it's fair share of scary backwater folk for a rather small area.
While not nearly as bad as those in a top ten big city it can still try your patience if you choose to live in these areas, to say the least. Actually, a walkscore map will also clearly show which side of the city is favored.