When I arrived in Lyon, France for my study abroad back in the day, it was my first time traveling by myself. I was sad, homesick, alone, and luggage-less (my bags didn't make it on the plane with me!).
Rather than stay in my hotel room and mope (infinitely more depressing), I spent the day walking around the city, trying to get my bearings. I eventually found myself at the Rhone River and saw the Hôtel Dieu on the other bank with the basilica perched atop Fourvière Hill in the background. Seeing that beautiful sight for the first time on that cloudy, overcast day reaffirmed that I wasn't making a horrible life decision and that I had so much wonder and opportunity before me.
What makes this my favorite travel memory [now] is that I now LOVE traveling by myself! I've been to 5 countries and many more cities in the U.S. and abroad traveling solo. I'm entirely convinced that I would have never grown so much personally, without my time in Lyon.