Does "Central Perk" cafe exist in reality? Or did it ever exist in reality? I am guessing they used a set for that cafe but is there a real one?
According to Wikipedia, Central Perk was a set at Warner Brothers Studios, so it wasn't real at the time the show was filmed. Reality, however, has caught up:
Now Central Perk not only exists, but does so in many locations.
As far as I'm able to learn, there was no single inspiration for Central Perk (ie. that existed before the show was created). The exterior shots of Central Perk were filmed in Greenwich Village, but there's no record of what that particular building is or was.
The rest of the show was filmed at Warner Brothers Studios in Los Angeles, so there wouldn't have been any interior location shots of Central Perk in New York.
Since the show ended, there have been a number of cafés opened around the world based on or inspired by Central Perk. Wikipedia has a list of these. There was also a café in New York called the DownTown UpTown Cafe Lounge that claimed to offer a 'Central Perk experience' but this has since closed.
So, in short: no. Central Perk never really existed, but has since been imitated countless times.