Unspecified European City (An Amphitheater, A Circus)
The story doesn't give us much in the way of specific geographical or chronological details, but we do learn that the hunger artist and his manager seek out various cities in Europe to put on their act. The details about the performance and the audience are so generic that the time period is hard to identify – and perhaps deliberately so, as the narrator keeps mentioning how unspecified "times" have changed. This unspecified "times" gives the story an almost mythical quality. If we do want to figure out why the public appetite for hunger artists has changed, we can't look to any specific historical event. Our only clue is in what "Europe" signifies for the text – which, again, isn't spelled out for us.
Most of the action takes place in two locales: when the artist is popular, his performance takes place in an amphitheater, but when his act falls out of fashion, he ends up in a circus. These two arenas aren't so different: both of them are places for popular spectacles, not really the right settings for the kind of high art the hunger artist is striving for. It's a bit like putting Pavarotti in the middle of a WWE match, or Shakespeare in the middle of a zoo. Well, that is, if you think what the hunger artist is doing really is high art.