I'm quite familiar with this topic, as I make it a point to run and explore every new city I visit. It gives me a chance to see the city through the eyes of a local and I see parts of the city that would never be highlighted on a map.
What comes with that, though, is constantly getting lost. As hard as I try to do an out-and-back, it almost never happens. I end up running in different directions either because something interests me, or, well, I just want to run in that direction. It's not so difficult in a more rural area where everything doesn't look the same and you can look at landmarks. In a city, well, that's where it gets interesting.
So how I find my way back when I get lost in a city? The good part about most cities is that they have public transportation. And with public transportation come maps. I just run from one stop to another, making sure I'm going to right way, until I end up back at my original destination.
I specifically recall this working in Dublin, Amsterdam, Cork (Ireland), Los Angeles and San Francisco. San Francisco was the first one where I realized I could look at the transportation maps, and it was when I had already hit the point of panic and a lot of miles after running through Golden Gate Park.
I guess it seems obvious now, but at the time, I had never thought of looking at bus or subway maps.
I mean, sure, I could ride public transportation, but then I'd have to figure it out and pay for it. Nah. Getting lost gives me more excuses to keep running, more excuses to keep exploring.
I typically won't ask for directions, either. That spoils the adventure.