The Medical Center is open during the following convenient hours: Monday-Thursday, 7 a.m. - 7 p.m. Friday, 7 a.m. - 5 p.m. Saturday, 8 a.m. - noon 440-816-4900 Urgent Care. Urgent Care services are now being provided through University Hospitals (UH) Urgent Care at both the Strongsville Medical Center and Brook Park locations..