A city is larger than a town. New York City, Boston, Miami, and Los Angeles are examples of cities. All state or country capitals are cities; cities usually have some significant political, economic or cultural importance. The word town refers to a smaller population center. And a very small population center - even smaller than a town - is called a village.
To complicate things, the central part of a city (especially the main commercial or business area) is called downtown. If you live downtown, you live right in the middle of the main action of the city - and it's more expensive to live downtown than to live in one of the other neighborhoods.