Yes, city states have been a common political entity around the world. Singapore is a modern example from outside Europe, the Middle East and North Africa.

Historically, Mesoamerica was home to many city states whose power rose and receded over the centuries. Major examples in central Mexico include Tenochtitlan and the earlier city Teotihuacan and Mayan cities such as Chichen Itza and Tikal. At the time of European arrival, Tenochtitlan had a population of more than 200,000 people, probably placing it among the largest cities in the world at the time.

There are problems of definitions here. What exactly constitutes a city state? Does it include cities like Cahokia that seemed to have been dominant culturally if not politically? How big does an entity have to be to be a city-state; were small independent native villages in New England city states? How big is too big to be a city-state; was imperial Rome a city state?

In any case, towns and villages seem to have been the earliest political entities around the world, long before the idea of a nation sprang up; nationalism as we consider it today in fact is a relatively recent construct. This has an intuitive sense to it. You start by seizing power of your city or town and its immediate surroundings, then expand to conquer neighbors until you eventually have something like a full-fledged empire. This is roughly how the Inca empire was built, radiating out from the central city of Cusco until it became one of the largest empires on Earth.