What is the term for an independent state consisting of a city and its
surrounding territory?

An independent state consisting of a city and its surrounding territory is called a city-state.

Explanation:

There are multiple types of independent states, and there are mutliple criteriums on which the definitions are made. A big portion of the smallest states, which are also very interesting, tend to fall into the category of city-states. This type of state is basically when one major city and its close surrounding territory make up the whole state.

Such states are nothing new, as they have existed since the development of the first civilization in Mesopotamia, through antiquity with the Greek and Phoenician city-states being an example, the Italian city-states during the Middle Ages, etc. Nowadays, there are still states of this type, and good examples are Monaco, Andora, Vatikan, and San Marino.

polar areas, such as antarctica or the south pole.