Staunton Clinic Patient Portal. This entry was posted in Main posts. ... 444 North Edwardsville Street Staunton, IL 62088 Phone: (618) 635-3800 Fax: (618) 861-6207. Hours: Monday 8 AM - 5 PM Tuesday 8 AM - 5 PM Wednesday 10 AM - 7 PM Thursday 8 AM - 5 PM Friday 8 AM - 5 PM Saturday temporarily closed. Staunton Clinic.