I've always found the term "postmodern" amusing, it's kind of like the way we refer to spandex, tinfoil spacesuits, blinkenlights computers and cardboard-box robots as "futuristic".
There's too many old cities still called some variant of "New City" like Novgorod (founded 882 years ago), Naples (founded as Neapolis in the 7th century BC), and Carthage (founded in the 13th or 9th century BC).
postmodernism just refers to a movement that came into existence (or at least into fashion) after modernism. it's at least as old as the 50s or 60s.