In the US the city is not a safe place for kids. Great for the 21-30 year old crowd (and older folks that didn't "grow up") since there are many great bars and parties, but there are no kid friendly places. I know several people out here in the suburbs who loved city living until they had kids. One kid under 5 isn't too bad, but as soon as the kid is school age you look at how bad the schools are and you get out thus ensuring nobody will try to fix the problem.
A large problem in discourse like this is relative terms. Specifically what people consider to be "city" or "urban" vs "suburban" vs "rural".
I live in an area of the US that the vast majority of US citizens would describe as "city" yet it doesn't conform to your description. The kids here get along just fine. But it's an important distinction because it would have been described as more of a suburb 100 years ago in that we are a few miles away from the heart of downtown.
And part of the problem in the US is that the US census has a very binary definition: urban and rural. Myself and two neighbors live on about 100 acres (not counting adjacent conservation land). We're considered urban. because we're about an hour drive of a fairly large city.
But a lot of people will pop up and say that 80% of the US is urban with the implication that 20% of people are living in the back of beyond in Wyoming and it's simply not true.
That's massively over-generalized. I live in Pittsburgh, which is not a huge city, but my experience is the exact opposite. My 8yo walks to friends houses in the neighborhood and to the park by himself sometimes. My 13yo is now switching from private school to the public high school, which is quite well-regarded. We don't live downtown, but our part of town has been an amazing place to raise kids. (Squirrel Hill, for those stalking Pittsburgh remotely. :). We chose not to live in the bars and parties areas because we're not 20. Cities are not homogeneous.
No kid friendly places? Like parks, museums, their school (I admit public school quality can vary enormously in urban areas in the US), bakeries, candy stores, etc all within a 20 minute walk for me? If all one sees in urban areas is bars and parties, maybe it is the people that leave that don't grow up.
My daughter has slept under the shark tank at the aquarium as well as with the mummies at the local cultural museum. The local university runs summer camps for everything from engineering to gymnastics. The Museums run programs, too. Her grade school has a thriving parent community because the parents stand together when school is let out instead of forming a long line of cars, I've made new friends myself this way (the number one complaint I get from parents that do move out is that they know no other parents in their kid's school). Because I walk everywhere, I don't ever deal with traffic.
I'm not saying it's perfect, either. Urban areas vary a LOT, including within any single city and within the country. My child's been directly exposed to poverty, homelessness and mental health issues, etc. I'm comfortable enough to explain the complexities of this to her, but some people would rather not.
This is not to criticize people who want to live in a rural or suburban life. I grew up in a small town and got myself out of there very quickly, mostly because I felt isolated and trapped growing up. But cities are very much places you can live in, kids and all.
Which city? IMO having public transit and good sidewalks would be amazing for older kids in the 12 to 16 range. I grew up in a small suburb, connected to the world only by a busy 40 mph street without sidewalks. I was basically trapped at home unless I could convince my parents to take me somewhere until my friends started getting cars when I was 16 or 17.