I grew up in a town of about 20,000 including the college. I rode bikes with a friend or a few friends (not alone) up I don't know half a mile? to the gas station to spend my allowance on candy, pizza, junk when I was 8. Maybe 9.
Rode halfway across town to the pool for the first time at 8 too but that was not with permission exactly
WITH PERMISSION I know I did it the summer I was 101/2. (I remember riding the 10 speed bike and I got that for my 10th b-day in Sept.)
as far as playing outside in the neighborhood, I know we were doing that at like 4-5, basically whenever you were old enough to know to stay out of the road. But like someone said in my neighborhood everyone knew each other, there were people keeping an eye out wherever you were. You weren't truly UNSUPERVISED if you were out of YOUR parents' sight.
where I live now, it would really depend a lot on what part of town I lived in and how far the closest park was how young they'd get to do that.
as far as playing out in the neighborhood---current neighborhood, if Z was in kindergarten at the school across the street I'd let him go over there and play with me having my window open to hear/see what's going on--I've got a direct view of the playground. but there are some potty-mouth kids that come around there, we'd have to have the understanding that he has to come home when the older kids come out.
the mall here, well, I was 13 or 14 the first time my parents dropped me and a friend off at the mall. (this is the mall in the town I live in now, over 120,000) I think i was 13 and friend 12. My friend's mom was PO'ed and thought we were too young then!
She went with us to that mall and another slightly smaller one, stayed in the mall shopping elsewhere until we were old enough to drive OURSELVES I think--and we are talking drive out of town at least an hour so I think we were actually 18 LOL.
Wandering the mall with the parents in another store or something, we did that in our small-town malls at maybe 9-10?
I think too it all depends on your kid and where you live. My current mall in this town, if I had a kid I could totally trust to not do anything stupid or be meeting up with any other kids who would be doing anything stupid, I'd say they could be out of my sight in a mall starting at probably 12.
to go there themselves, when they can drive there probably. I *might* consider a drop-off and pick-up at 13-14. It's more that I don't see a NEED to go wander around the mall, you just don't know what might happen, who they might run into, or they might find out their trusted friend is a klepto when they get caught somewhere. (I would HOPE my kid would resist peer pressure to join in that activity, but that is another thing you don't know--if you are IN the mall, it would be easier for them to leave and find you than if they've got to call you and have you come across town to pick them up? and the idea that the parent is there would curb that kind of activity?)
I figure if I'm trusting them with a car, then they can also be trusted to use good judgment on where they go and what they do with the car. Otherwise why am I allowing them to drive??