(covers information from several alternate timelines)
In 2259 of the alternate reality, Thomas Harewood owned a hovercar. He used the vehicle to drive himself and his wife to the Royal Children's Hospital to see their daughter, who was terminally ill. (Star Trek Into Darkness)
In 2371, when the USS Voyager brought aboard a 1936 Ford truck, Harry Kim mistook it for an early hovercar. However, Tom Paris stated that particular automobile was about a century too early for that to be the case. (VOY: "The 37's")
In an alternate timeline, shortly after Jean-Luc Picard and Geordi La Forge arrived in England with the intention of seeing Data there, a hovercar was driving to Cambridge University, where Data was living. (TNG: "All Good Things...")
Background information EditThe script of Star Trek: First Contact mentioned the hulks of now-useless hovercars lying corroded in the streets.
Wheeled vehicles apparently continued to survive in specialized roles even after hovercars became ubiquitous. Examples include the wheeled truck-like vehicle used by the Arctic Archaeology Team in 2153 in ENT: "Regeneration" and the Argo buggy in use by Starfleet in the late 24th century in Star Trek Nemesis.