No. In antiquity, or at least in the Mediterranean, the idea of public transport would have been both alien and impossible. Even the largest cities were generally quite packed together, with an area vastly smaller than their population might indicate (leading to a horribly high population density)--even the ancient urban site at Rome can be walked across in a relatively short time without much effort. Few people had much reason to travel long distances within the city anyway. Shopkeepers and skilled laborers could afford to live in permanent arrangements, and usually lived above or near the establishments at which they were employed. The majority of the Roman urban population was composed of semi-homeless day-workers who drifted through the city daily looking for work. These people might have to go fairly long distances across the city to find work, although I can't imagine the odds were good that they'd get it by the time they got there. The majority of urban laborers, certainly at Rome and elsewhere as well, lived barely above starvation in horrible sanitary conditions and with essentially nothing in the way of comfortable accommodations. Families could hardly afford food, the cost of paying for transportation wasn't even a dream, it was a fantasy. At Rome following Caesar wheeled vehicles were forbidden within the city in the day, and long before that traffic in the city had been limited to pedestrians and people riding litters or sedan chairs--neither of those two latter options would have been available to all but the very rich, and the idea of the state subsidizing thousands of public litters, which were extraordinarily expensive, is a little ridiculous.

This is a very broad question, was there any particular civilization or time period you had in mind?