Sailing to Byzantium, by Robert Silverberg (epub/Kindle/pdf)
On 50th-century Earth, people live in recreations of historical cities. Currently the cities are Chang-an, Asgard, New Chicago, Timbuctoo and Alexandria. They are periodically dismantled and replaced with a different city; there are never more than five. They are populated with "temporaries", who live as they would have done in the era of the city. "Temporaries" seem to have been created to provide the impression of realism.
Charles Phillips and his partner Gioia are in ancient Alexandria. Phillips is from New York of the year 1984, and does not know how or why he is in the 50th century. Gioa's people never work: they see the sights during the day and go to parties in the evening. They soon move on to another city....