If you refer the map in this answer https://scifi.stackexchange.com/a/5710/1148 you'll see that all of these cities have a place on the map independent of real cities. However, your question reads more wanting to know the original inspiration for the cities.
Metropolis:
Within the DC Universe, Metropolis is portrayed as one of the largest and wealthiest cities on Earth. Since then, Metropolis has become a city inspired by New York City, Chicago, Cleveland, Detroit, Toronto, Vancouver, and Los Angeles. Most of the notable landmarks in Metropolis are based on real-life landmarks in New York City.
Metropolis appears to take elements from many of the largest cities located in North America. This helps to establish itself as perhaps the grandest city. I imagine this is so readers from large cities can both relate to Metropolis, but still be impressed by its grandeur.
Gotham City:
Before Detective Comics #48, Batman's adventures were said to happen in New York City. Gotham is known to be architecturally modeled after New York City, but with exaggerated elements of the styles and derives its name from a sobriquet for that real world city, first popularized by the author Washington Irving in his satirical work Salmagundi (1807).
As the quote says in 1807 Salmagundi nicknamed New York City "Gotham." As a result there are a number of businesses, media outlets, and artists who use the name in association with New York City.
Central City:
In the 1970s, Central City was stated as being located in Ohio, where the real-world city of Athens, Ohio, would be (as shown in Flash #228 in 1974). Bob Rozakis' Ask the Answer Man column also stated that Central City was located in Ohio.
Since Athens is the largest city in Ohio, at least during that time, Central City may have been patterned after it.