While our mythology is younger than that of other countries, I think we do have one and it would be interesting to explore and expound on it in fiction. American "mythology" is not the "class of super-natural / para-normal beings" ie. fairies, goblins, etc. type. Ours is the interesting cast of lunatics type like the Norse or Greek gods. On both a national and a local scale there are historical and literary figures who have developed beyond the facts of their origin. They populate American myths and create Americana.

On the local note, the San Francisco's "spirit" is good hearted whimsy and eccentricity. We are named for a well meaning nut job who gave up fabulous wealth to hang out with animals. Our most beloved historical nut is a man who believed himself to be an Emperor, and we let him and encouraged him, and still, more than a hundred years later, revere him as our emperor.