Talking about worst cities is depressing. Nobody wants to visit Topeka or Detroit anyway.
For me this question is surprisingly easy. Istanbul stands out far more than any other city I have visited. Istanbul offers anything a traveler would ever want; history, culture, nightlife, good food.
History: It is where East meets West. The Greeks, Romans, and Ottomans have all called it home. The history here is unparalleled, I would even place it over Jerusalem. Religion may call Jerusalem home but Istanbul has been the city at or near the center of power for 2500 years
Galata viewed from Sultanahmet
A walk around Sultanahmet is like being in the history books
Hagia Sofia is the 2nd largest church in the world, built under Justinian in 576 when the Romans called Constantinople home. It was then turned into a mosque under the Ottomans and is now a museum
Turn around and you are staring at the blue mosque which was built between 1609 and 1616
Also in Sultanahmet is Topkapi Palace which is my favorite of the three but not as picture friendly. In addition there is an underground Roman reservoir and the Grand Bazaar which is one of the oldest and largest in the world covering 58 streets. Takes 3 days to see Sultanahmet proper and that is just the tourist crap
Then you got Istiklal Street which is lined with shops, restaurants, and bars. According to Wikipedia 3 million people visit every weekend. You can get lost in the side streets, order tea, play backgammon and smoke some sheesha. The clubs go all night and you can find anything you like.
The food is delicious. Doner ftw for those on a budget
I dunno if it is Turkish but it's the only place in the world I've ever seen it, and I'm American (looks like something we should have). Waffle taco filled with ice cream toppings!
That is an introduction to my favorite city to visit. Now post yours, and try to include some pictures!