The Dark Zone doesn't end at the northern wall of DZ06. One player has broken out of The Division's intended playable area and documented their journey through the northern reaches of the Dark Zone and beyond, much like those players who went traipsing up to the ethereal floating tree land formerly known as Central Park.
Reddit user CodeDux explored the area and found mostly long, empty streets. It wasn't all desolate, however - certain intersections are filled with cars, while the eastern checkpoint to DZ08 was complete with torn, bloodied fortifications. They also found a few bright blue "Clue Placeholders", which are presumably developer tools used to indicate where collectible items like voice recordings could go in the future.
Currently, players can only explore DZ01 through DZ06, a series of cordoned-off blocks that get more intimidating the further north you go. A map found in the game's United Nations building lays out other zones, including some kind of stronghold. I should note that that these non-accessible (in theory, if not in practice) areas may just exist as flavor and to give you something to look at over the walls, making the game's world feel larger than it actually is.
On the other hand, The Division's second free content update will add a new "Incursion" mission set in Columbus Square. The developer-intended map doesn't currently extend that far uptown, so some of these "inaccessible areas" may get a proper debut at that point.
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This is where that DZ08 entrance is located on the map.
And here's a long, deserted street inside that area.
And here's right about where Columbus Circle should be, with its famous fountains and statue.
Though, for now, the area still seems to be mostly empty streets.