Skeptoid - Brian Dunning turning a skeptical eye toward various myths, fake science, and common logical fallacies.
Science Faction - A science/comedy podcast that is both informative and funny if you can handle some juvenile humor and non sequiturs.
Stuff They Don't Want You to Know, Stuff You Should Know, Stuff You Missed in History Class - The "Stuff" series of podcasts are all pretty chill. The name describes the content. Informative, or entertaining, but not so heavy that it will keep you awake.
Beyond that... I have struggled with insomnia since puberty. This isn't my first rodeo. :(