Well, most Trek sources seem to agree that Earth is paradise in the TNG era. I don't recall any specific references to cars in the episodes (and I have all of TNG, DS9, and VOY...), but I would think cars in the 24th century would be like horse and carriage is today. I guess nobody would use a car for transportation as they already have transporters or shuttles that are infinitely more useful, but there cars can have other functions than as a means of transportation. I don't think it would be inappropriate at all to have cars on Earth as long as it's for nostalgic reasons. Note how much Tom Paris loved old movies and cars on Voyager? Well, imagine there are groups of people with similar interests all over Earth... That way you would have cars here and there. Sure, there would be few and they would be seen as antiquated, but then that just means you won't have traffic
"We think we've come so far... Torture of heretics, burning of witches - it's all ancient history. Then, before you can blink an eye, suddenly it threatens to start all over again..."
- Captain Picard, "The Drumhead" (TNG).