It depends.
For example, Paris is currently, in my opinion, the most overrated city in Europe.
It also has major security problems.
Among other things, by gangs of immigrants from Africa.
But generally all big cities have dangerous neighborhoods.
Of course, there are safer cities and less safe ones.
Do you live in the USA in a big city? If so, I guarantee it won't get much more dangerous.
As for other examples, there are many pickpockets and other people like that in Barcelona.
This is due, among other things, to the fact that it is a popular tourist destination.
If I can recommend something, it's not necessarily that you focus on the big cities.
Smaller towns can also be beautiful, pleasant and much safer.
For example, in France I would avoid Paris like the plague and look for some nice, picturesque towns.
Don't be afraid of Eastern Europe and the Balkans either.
We're not that bad ;).
Our countries also have beautiful architecture, beautiful landscapes, etc.
Just don't limit yourself to the mainstream.
This is a very big tourist mistake.
Of course, it all depends on what you are looking for and what you want.
An individual matter.