Nicosia/Lefkosia
Cyprus has the last divided capital in the world, split almost evenly between the Turkish north (Nicosia) and the Greek southern half, known as Lefkosia. This capital is most famous for its "Green Line," the division defined when the British drew a green line on a military map, making the very real separation.
The most arresting physical feature is the Venetian Walls surrounding the Old City. Although a beautiful and very safe city normally, travel guides still advise lone women to avoid the area at night, which is a pity.
For more on the green line