All alone, at a bus stop, or waiting for a friend. It was torture just standing there as a teenager in the 90s. Had to start smoking.
I'm not saying smartphones made me quit smoking but mp3 players did give me an excuse to put headphones on and at least do something while waiting for public transportation and the like.
I did own a walkman before that but strangely it was never with me when I needed it, because of its size. It was a chore just to plan to bring my walkman anywhere.
Edit: This made me realize the first music player that was most regularly in my pocket was a Sony minidisc player. I also loved the format because it seemed so futuristic.