What does this have to do with writing? I believe that good writing comes from good mental health which comes from good physical health. When I'm tired and out of shape, my thinker doesn't want to think. Exercise is a good time to get away from the other distractions and open yourself to a period of meditation and imagination. I can mull over problems in the plot or imagine new characters or concepts.
My Polynesian gladiator story was a mix of reading a book on roman gladiators and watching a documentary on the conquest of Hawaii by an aggressive expansionistic tribe among the islands before the USA came knocking on its door to become a US Territory, while working out at the gym (wow what run-on sentence, and I call myself a writer).
This morning before the 5K I was writing my Paleolithic (though its probably actually Neolithic) story and was writing about the physical contests and games the clan did at its annual Summer gathering. I wrote about a spear throwing contest. While running the 5k I thought to myself that they would probably have foot races too. So in the final draft, you might see a foot race, or at least mention of it in passing. It all depends on which elements remain relevant to the plot or to character development.
Inspiration can come from anywhere and everywhere. Let yourself be influenced by what's around you. And live healthy so that your mind can be fit for the sport of writing.