What is the eastside medical center? The Eastside Medical Center, located in Snellville, GA, is a health care institution that offers medical and surgical treatment. The Hospital provides emergency care for injuries, sudden illnesses, and severe illnesses in Snellville.What is the mailing address for emory eastside medical center? The current location address for Emory Eastside Medical Center is 1700 Medical Way,, Snellville, Georgia and the contact number is 770-979-0200 and fax number is 770-736-2395. The mailing address for Emory Eastside Medical Center is 1700 Medical Way,, Snellville, Georgia - 30078-2195 (mailing address contact number - 770-979-0200).Why choose eastside internal medicine? Since we are part of the Center for Primary Care, we work closely with the region's top specialists at Highland Hospital and the University of Rochester Medical Center. Eastside Internal Medicine provides 24-hour telephone coverage for emergencies and urgent problems.