The OP's question always morphs into a what age is appropriate discussion. On another website I visit there is along conversation about the toys we had a kids, lawn darts, REAL chemistry sets, airplanes that flew on a string with us as the pivot point, model rockets, etc.

When I was in 2nd/3rd grade I rode the bus home, walked behind a small strip mall to our apartment and let myself into out place. I had a key. AKA a Latch Key.

Sometimes I would forget and have to run to the apartment managers for a key.
At the same place I used to disappear into the woods to play for hours.
In fourth grade, different city/state, I was riding by myself to school a couple miles away and had to cross a major four lane road. And I would ride my bike all over the place. Chase rabbits in the cotton fields with my dog. Basically just disappear and only return home for food, drink, and sleep.
When visiting my family in Orlando my grandmother lived two houses down from a school. Back then the schools were not surrounded with fences and I would ride/walk to the school and play for hours.
My other grand mother lived on a lake in Altamonte Springs. My cousin and I spent hours and hours almost every day swimming in that lake. Throwing muck at each other and other kids. Somehow I managed to survive the amoeba and gators. It was a great childhood that my kids will not have since we don't live on a lake. It was great experience. We even went fishing. On a boat. By ourselves. At night.
My cousin is two years older than me and I am certainly the most responsible of the two.

We would walk to the mall to see movies or go to the arcade. I had to be no more than 13/14 and he had to be no more than 16. We saw the first Star Wars movie at the mall. It was so good we stayed and watched it again!
Sometime around when I was 10 or so my mom and aunt would let the two of us go off by ourselves at MK. We would check in every few hours for food and more E Tickets!
Now the point of all of the previous was that I had lots of freedom. I don't think that many kids get that freedom anymore. I also admit that when I see young kids, especially girls, walking by themselves it makes me nervous. I used to live near a park in FLA were a serial rapist was attacking women in a very public area in broad daylight. One attack was on a jogger on a busy four lane road the middle of the day.
One day our kids will go to the parks by themselves if they want to do so. Not sure the age but I would guess it will be before they are 18. Our oldest has already figured out the buses. The youngest almost can as well.
Being at the pool after the age of 12 does not bother me. GETTING to the pool is what bother's me. At a resort there are lots of rooms where ANYONE can be easily snatched into. Never heard of it happening but its a risk.
One of the attacks against children at the water parks was when the man "bumped" into the girl in one of the wave pools. The father was near by and the daughter told him what happened. The father and lifeguards found the man and held him until the police showed up.
Later,
Dan