The AP recently had a story in which they went to "the heart of Trump country," specifically Sandy Hook, Kentucky, "isolated in the foothills of the Appalachian Mountains." Apparently a number of people said they were tired of hearing about the Trump voters in Appalachia mourning for the days when coal was king, according to this story by Philip Bump, and observed that plenty of Trump voters could be found in affluent suburbs. I have made the same complaint myself in the past, but as Bump pointed out, in Elliott County (where Sandy Hook is), there was a large swing to Trump. So if you're looking for people who were attracted to Trump, rather than people who just voted for him because he was a Republican, it's a defensible choice.
I looked more systematically, using these county-level election results for 2012 and 2016. These were compiled by volunteers, so there may be some errors, but I checked some cases and they seemed good. In 2012, the mean county-level Republican share of the vote was 59.8%, and in 2016 it rose to 63.5%. This shows two things--that the Republicans tend to do better in the less populous counties, and that this tendency became stronger in 2016. There are about 3,000 counties in the United States; here is the geographical distribution of the 100 with the biggest pro-Republican swing between 2012 and 2016:
West Virginia 4
New York 3
North Dakota 2
South Dakota 1
Elliott County had the biggest swing. The counties that moved towards Trump were overwhelmingly in the Midwest (broadly defined)--there were only a handful in the Northeast, none on the Pacific coast, and none from any Southern states except Tennessee and Virginia. A significant number are in Appalachia, but most of them aren't. I don't know anything about most of the counties on the list, so I can't offer any thoughts on what they have in common, but it seems like journalists looking for "Trump country" should broaden their focus--in particular, Iowa deserves attention. The one thing I can say is that they mostly had small populations--the biggest was Schuylkill County, PA, whose biggest city is Pottsville (home of some of my ancestors).
I also calculated the counties with the biggest swing to the Democrats. Their distribution:
North Carolina 4
New Jersey 2
New York 2
New Mexico 1
A lot of large cities appeared on the list--Los Angeles, New York, San Diego, San Francisco, and Dallas counties, as well as Harris County (Houston), Fulton County (Atlanta), and King County (Seattle). There were also some affluent suburban counties, like Fairfield (CT), Westchester (NY), Somerset and Morris (NJ), and Johnson (KS). They were less geographically concentrated than the counties with the biggest Republican swings, The shifts were also smaller--the biggest swing to the Democrats was in Parmer County (TX), where the Democratic share went from about 20% to about 30%. There were about 350 counties in which the Republican share increased by more than 10%.*
The one clear thing is that the urban/rural split got bigger, and the urban swing to the Democrats was not just in "blue states." An interesting question is what happened in Georgia--none of the nearby states had nearly as many counties that shifted to the Democrats.
PS: This is a convenient place to look at results for individual counties since 1920.
*If you consider Republican losses, the contrast is less striking--there were a number of counties in Utah and Idaho where the Republican share dropped by 20% or more, presumably because of shifts to Evan McMullin. But it's still substantial--there were only about 40 counties in which the Republican share dropped by more than 10%.