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This is a short story (definitely not a novella) set in 'the future' where cities are connected by massive conveyor belts that people hop on/off and one of them breaks down or gets damaged. I think there's a scene set in a diner. I believe the story was from the 40s or 50s. It was on an audio book I had back in the mid 90s.

I agree with Mike Stone's answer that this is most likely "The Roads Must Roll" (1940) by Robert A. Heinlein. However, considering you listened to it as an audio book there is a chance you may have actually listened to one of the radio shows that played it, either Dimension X (1950 - 1951) (episode aired 1950) or X Minus One (1955 - 1958) (episode aired 1956). Both of which are free to listen to online publicly.

In the first section of the narrative, the protagonist Larry Gaines is entertaining Mr. Blenkinsop, an Australian who is looking into Road technology on behalf of his government. Gaines's explanation of the Road machinery to Blenkinsop is a device to bring the reader into the world of the Roads.

Larry Gaines, Chief Engineer of the Diego-Reno roadtown, is dining with a guest from Australia, Mr. Blenkinsop, in a moving restaurant on the road, when one of the moving sidewalk strips unexpectedly stops. This causes a chain reaction of people falling from the stopped strip onto the fast moving strips next to it, and vice versa. The entire length of the Road becomes a scene of carnage. Gaines learns that the stoppage was sabotage and that the technicians who maintain the Stockton section of the road are responsible. They have been persuaded by a radical social theory, Functionalism, that their role in maintaining the nation's transport infrastructure is more important than that of any other workers and that they should therefore be in control. Blenkinsop is left behind at one of Road stations as Gaines takes charge of the advance on the Stockton office.

There is a brief summary for the X Minus One episode which outlines the basics of the story:

Story of future transportation when rolling roads move people and goods, and the men who take care of them. The script is by Ernest Kinoy. The cast includes Wendell Holmes, Ralph Belland many more. Writer: Robert Heinlein

Almost certainly Heinlein's "The Roads Must Roll". Actually the road doesn't actually break, but is just brought to an abrupt stop, but there are still casualties.