Answer:
Answer
It would depend on the definition of a "city" as opposed to an unincorporated suburb or county location. In 2002, there were 19,000 municipal governments throughout the US, but as many as 30,000 incorporated cities.
There are over 43,000 places with unique zip codes, and probably no "cities" without their own zip codes. Many large cities have 2 or more zip codes. A guess would be around 20,000 to 25,000 including larger towns and such.