My native city, Harrisburg PA, was (and as far as I know, still is) like Gaul, divided into three parts: Downtown, Uptown, and The Hill. The Hill is a geographically separate section at the top of a broad high hill which rises up from Cameron (11th) Street at the eastern end of the city. Downtown is the area from the river to Cameron St. going W to E and from the south end of the town about 15 or 20 blocks or so north and comprising the central business district and the state capitol complex. North of Downtown is Uptown, much of which was the high-class residential area. (No longer -- there are no high class areas in Harrisburg any more.) So, like NY and most other cities, Downtown usually connotes the most crowded, busiest and lively areas of a city and Uptown generally connotes a wealthy or higher class area.