There where many greek colonies outside Greece proper, many of those where pretty important.

Marseilles, Syracuse, Taranto for example. They typically were founded by an expedition from a single original city, with which they retained close ties, but quickly became independent.

Of course they were all subsumed by the romans, but only after several centuries of existence as city states.

The ancient Phoenician cities Tyre and Sidon had traditionally been independent city-states, and they retained some of that identity, although being conquered multiple times in that era. The Berber people living in southern Libya also had a network of prosperous trade-based city-states called the Garamantes, between 500 BCE and 700 CE. Pre-Colombian Mesoamerican societies like Aztecs and Mayans were also dominated by city-states.

If you aren't talking strictly about the Classical era, there have been many others. Early Near Eastern civilization in Sumeria and Egypt was based on city-states. There have been merchant republics in Italy (Venice, Genoa, Pisa, Ragusa, and others), the hanseatic free cities of the Holy Roman Empire, Novgorod, and later on, around the Horn of Africa and along the Silk Road in Central Asia. Many people would also consider modern states like Vatican City, Monaco, Singapore, and Liechtenstein to be city-states, as well as highly-autonomous regions like Hong Kong and Macau.

A number of oasis city-states existed along the silk road, on the fringes of the Taklamakan desert, in what is now known as China's Xinjiang ("New Frontier") province. Historically, they were often incorporated into larger local states, whether Chinese or Inner Asian (ie: the Mongolian Empire). Currently they are, as mentioned earlier, under Chinese rule, which dates back to conquests during the Qing dynasty.

Axum (Aksum) has been a stable site of human development since 400 BC, and was the capital of the Kingdom of Aksum - and a major trading partner with the Greco-Romans. In fact, the script of the Kingdom of Aksum, Ge'ez, is based on Greek.

Edit: Another notable City-State turned kingdom is Meroe.

What about Palmyra? Yes, it was briefly capital of an empire, but I think it was a city state for a long time before that.

The Mayan city states.