Trying to remember my childhood, it was soooo long ago...
Pretty sure that by the time I was 10, I had free reign of the entire town (trying to remember the movies that came out that I went to sans parents, I think that's about right). This meant being able to go several km from home without question, or even ability to really stay in contact - payphones for emergencies but this was a couple of decades before every kid had a cellphone. Hell, with the advent of cellphones I'd be inclined to give kids MORE freedom, because at least they can easily call for help if they get lost/in trouble/etc.
Now, I grew up in a smaller town (7000ish people) which helps parents' comfort levels a lot, plus we walked more than a km to school every day anyway so they quickly got used to it. That being said, we had proportionally just as many creeps in town as I've seen in any city (maybe even moreso, small towns can be WEIRD). Agreed with the comment that crossing the street can be more dangerous than anything, and in a city, it's much worse.
One thing I will say - get your kids used the concept of getting around on their own, as young as possible. Or else you're going to be faced with the inevitable consequence - providing them a vehicle the second they're legally able to drive. Kids I grew up with who weren't allowed to learn how to walk/bike/bus anywhere are insanely car-dependent and by the time they become teenagers, it's their god-given right to have a car!! Plus, most of them have absolutely no sense of direction. Learning the city from driving alone is a great way to ensure a dependency on GPS in later life.