Copernicus City was a city located on Luna, Earth's moon.
In 2324, Beverly Howard was born here. (TNG: "Conundrum")
According to unseen material created for the Picard family album in Star Trek Generations, the reception of Beverly's and Jack R. Crusher's wedding was held in the Phobos Inn in Copernicus City on July 20th, 2348.
Copernicus City was likely named after the homonymous crater on Luna, in which the city might be located, which itself is named after Nicolaus Copernicus, a European astronomer of the 16th century. Star Trek: The Official Guide to Our Universe (p. 21) suggests Copernicus City was "an early community situated inside [the] crater Copernicus."