The two metrics that have been used for this are HCAPS and Press-Ganey which both not only look at the patient experience in the ED but specific modules of their ED experience (interactions with registration, RN, MD, medical imaging, lab, etc). These metrics also look at the entire patient experience as an inpatient (admitted patient) as well.
We have a survey to measure patient satisfaction with primary care physicians. You could probably modify it to use with emergency-room settings. The link for downloading the article is attached.
I believe for emergency departments, speed of checking in, how quickly the patient is seen by a doctor, the attitude of the doctor, nurses, etc. will be very important.