In Luann, which is currently the most interestingly-plotted comic strip that my newspaper carries, the college-age Luann is preparing for a trip to New York with a couple similarly-aged friends, and her parents are fretting about this first non-parentally-supervised trip and reminiscing about their own.
I suppose mine depends on precise definitions.
When I was as young as 8, I was taking full-day trips by bicycle to explore the rugged hills near our home. My parents let me do this because they knew I wouldn't get lost (I was an assured map-reader even then) and could be relied on to be home by dinner. My mother would pack me a bag lunch.
How about a little farther away?
I was all of 15 when my parents packed me on a plane by myself and sent me off to visit my grandparents. We were actually on a cross-country vacation at the time, and I missed the last leg, which was fine: by that point in the trip, spending another week cooped up in the motor home with three little brothers had lost its appeal. This was the trip when my grandfather took me on a private tour of the brewery for which he was the leading distributor, with the president of the brewery as our guide; fortunately I was too young to partake of the product and have to pretend I liked beer.
Overnight without parental supervision?
That depends if college dorms count. I moved into one at 18.
How about without any in loco parentis at all?
That would be when I was 19 and started attending science-fiction conventions. For my first, I took a bus the 40 miles to the City where a friend who lived there picked me up and drove the remaining 80 miles or so to Sacramento where Mythcon was. Another friend drove me back. Several other group expeditions followed, some involving me driving, but the longest was a large group expedition to a Westercon in Vancouver by train.
My first big totally solo trip that I can recall was to Britain at the age of 22. I attended the Worldcon in Brighton but I did many other things, and drove as far as North Wales and Yorkshire. Surely this wasn't the first time I rented a car, but I can't think offhand of when before I might have done so.
The year after that I moved to Seattle for grad school, and the following year acquired my first car entirely of my own, as opposed to an extra parental car for which I had privileges, and since then all my traveling has been of my own making.