Basin Care Family Medicine. Basin Care Internal Medicine. • 8am - 5pm, Monday - Friday. • Closed on Saturday and Sunday. • Walk-in, No Appointment Necessary. 1816 North Midland Drive, Midland, TX. Phone Line: 432-699-5111, FAX: 432-699-0773. • 8am - 5pm, Monday - Friday. • Closed on Saturday and Sunday..