Everything looks good under the car, nothing out of the ordinary. I have not pulled my drums yet to see if there was something wrong with them. What should I be looking for if I pull the drums apart? Both wheels spin very smoothly and quietly when jacked up.

There should be just a little rubbing against the pads when you spin them, it sounds like your rears need adjusting anyways. As for what to look for; theres not alot in there - loose or broken parts would be about it.

Drum brakes here.

Check for loose/misadjusted springs.