A Torrent of Faces, by James Blish & Norman L. Knight. Since I haven't read this, I'm quoting the flap copy from a hardcover edition for the best plot summary I could find:

In the world of 800 years in the future, one thousand billion people are kept reasonably content in a complex and completely automated society. But now the approach of a 50 megaton meteor threatens a vast natural disaster and the destruction of peace and order. The salvation of the world falls on the shoulders of Biond Smith, chief of the Disaster Plans Board, whose task is further complicated by his own personal loves and hates and those of his subordinates and superiors, the governors of the world, at Prime Center. As the meteor moves dangerously closer, Biond and his aides find themselves at the Barrier-Hilton, a shipwrecked floating luxury hotel; the monster megalopolis of Novoe Washingtongrad; a sealed biological preserve; a convention of the Jones family with one million in attendance; the depths of the sea; and in a strange combination of slum and fun house where he finds an unexpected answer to part of his dilemma.

The credits reveal this is a "fix-up," revised and expanded from 3 novelets - "The Shipwrecked Hotel" (August 1965) and "The Piper of Dis" (August 1966) - both from Galaxy, plus "To Love Another" from Analog (April 1967.) What the credits don't mention is that this is all some sort of sequel to Norman L. Knight's "Crisis in Utopia" from 1940 in Astounding. That has been anthologized a couple of times, so you might be able to track down a copy...