A city is a place where people live, work, experience, go out, party, study, ... In short, there's always something to do in a city.
Do you live or work in a city? Are you a city guide? Do you know the best places in your city to eat or shop? Do you as a city council want to keep your residents up to date of everything that's going on in your city?
Then a .city name is exactly what you are looking for.