About Old Town Clinic. ... Old Town Clinic's 20 physicians cover 14 specialty areas of medicine. Old Town Clinic Office Locations. Old Town Clinic. 727 W Burnside St Portland, OR 97209 (503) 228-4533. ... Practice Website: www.centralcityconcern.org. Accepting New Patients: No. Medicare Accepted: No. Medicaid Accepted: No. Physicians at this ....