There is one city that Skopje reminded me of. When I visited Casablanca (a city in Morocco) I had a similar feeling, but the line between two sides of the city was not so obvious there (you can read more about the "Moroccan city of contrast" in this post).
In Skopje the river Vardar acts as a barrier between the two worlds. However this barrier can easily be breached using the Old stone bridge, linking the two sides for centuries.
On the right side of the Vardar river is the new town. The main city square looks quite new and could be easily placed in some other modern European city. The nearby streets lined with cafes and most of the famous trademarks are sold in many of the very European looking shops. Unfortunately, judging by the average monthly income which is somewhere around 400 Euros, not many locals can afford to go shopping there. Not only the looks but also the prices in these stores are also very European.
On the left side of the river stands the old - Albanian part of the city, overlooked by an old fortress (it is supposedly being rebuilt for quite some time now). If you get lost in the grey streets, you will find the old bazaar easily. With tons of junk sold there, it definitely has a special kind of charm. If the right side looks European, the left side of the river definitely looks at least a bit Asian.
Rumor has it that the police don't patrol the Albanian side of the river. I didn't feel unsafe for a moment, but then again I did not try to wander these streets by night.
My intention is definitely not to make people turn away from exploring "the darker" side of the city.
On the contrary... If you get a chance to visit the city of Skopje, I strongly suggest you take a trip to the other side of the bridge and also get a glimpse of the old charm.
Apart from all that, there are also other things enforcing this feeling of contrast. For instance new and shiny buildings stand right next to collapsing old grey houses.
Even those new buildings usually only look nice and shiny from a safe distance. If you take a closer look you can usually find quality materials put together in a hurry and without much thought. This was also the case with our rented apartment. It had two nice bathrooms with a leaking bathtub/shower in each.
The building our apartment was in had a fancy video intercom at the front entrance and the front door could be opened via a numerical pad. In theory that is...
In reality none of those things actually worked and when the door bell rang, one of us had to walk five stories down to open the front door manually.
Another instance of diversity are definitely cars. One can see a great variety of those in Skopje. They range from the latest models of BMW and Mercedes-Benz to old Zastava Yugos and even ancient 750s.
The list just goes on and on...