Here in the United States, central areas of cites tend to be zoned for high-rise office, apartment and condominium buildings. This reflects pre-zoning practices in places such as New York City where new, larger buildings replaced older structures as market conditions evolved. Zoning laws and, later, preservation rulings have tended to preserve certain older buildings, deservedly or not.
In any case, almost no really large North American city that I can think of has an extensive "old town" district comparable to what can be found in Europe. Yes, a few preserved areas exist including parts of Charleston and Savannah in the South, Boston's Beacon Hill and Back Bay neighborhoods, and Québec's district within the wall. There might be a few others, but they don't come to mind as I write this.
From what I glean from photos I randomly notice, American practice is followed in much of the developing world where skyscrapers sprout like mad. Shanghai's Bund is still recognizable, but it is encroached by a field of megastructures across the river in Pudong.
That leaves Europe which, as I noted, has some major cities with large preserved areas. But how many large European cities actually have extensive areas that are largely untouched by skyscrapers or other significant modernist structures?
[Scratches head, rubs chin] Umm. There's Copenhagen, where much of the skyline in the old part of town is as flat as the terrain. And Vienna, which has a few modernist buildings inside the Ring -- but no high-rise buildings in that area. Both of these cites do have skyscrapers. But high-rise, modernist-style buildings are not permitted in the old city centers; they are segregated in areas a few miles away.
Below are examples of cities where tall, modernist buildings are found and not found in old city centers.